SELF  INSTRUCTION 

IN 

NAVIGATION 


TO  WHICH  IS  ADDED 

SOME  USEFUL  MISCELLANEOUS 

INFORMATION  INCLUDING 

ILLUSTRATIVE  CUTS  ON 

URULES  OF  THE  ROAD" 


BY 

HENRY  L.  THOMPSON 

MASTER  MARINER 

LATE  LIEUTENANT,  U.  S.  N.    ('98) 


PORTLAND 

PRESS  OF  SOUTHWORTH  PRINTING  COMPANY 
1916 


Copyright,   1916 


PREFACE. 


The  writer  of  this  book  has  endeavored  to  eliminate 
higher  mathematics  from  the  navigational  work  and  use  plain 
English  instead  of  formulae  that  prove  so  confusing  to  the 
man  who  has  not  been  educated  along  these  lines ;  to  such  a 
one  Bowditch  might  as  well  be  written  in  Greek.  The  skilled 
navigators  are  requested  not  to  criticise  this  work  for  it  is 
not  written  for  them,  but  for  the  ones  who  are  struggling  to 
inform  themselves  although  meeting  with  indifferent  success 
and  much  discouragement.  It  would  seem  that  any  such 
men  might  take  up  the  study  of  navigation  by  means  of  this 
book,  and  if  Chapters  1  -  6  are  carefully  followed,  and 
studied,  the  results  are  bound  to  be  good.  Let  those  who 
think  they  can't  get  ahead  because  they  haven't  been  as  well 
educated  as  might  be,  take  courage  and  start  a  systematic 
study  of  these  pages  beginning  with  the  Day's  Work.  Don't 
worry  over  the  formulae  in  Art.  1  (a  and  b)  for  they  will 
be  found  to  work  in  all  right  when  needed. 

Chapter  V  is  a  practical  illustration  of  how  these  various 
problems  ought  to  be  applied  in  practice  on  an  ocean  steamer 
and  it  is  believed  will  prove  helpful. 

The  mastery  of  the  problems  in  this  book  may  kindle  a 
desire  to  go  deeper  which  Bowditch  can  satisfy  at  any  time; 
but  for  practical  navigation  it  is  not  necessary,  for  there 
is  enough  here  to  take  a  ship  anywhere  in  the  world. 

Chapters  7  and  8  have  been  put  in  more  for  the  amateur 
than  anyone  else ;  at  the  same  time,  the  motor  boat  man  or 
yachtsman  may  investigate  the  whole  book  with  profit  to 
himself.  The  study  of  the -Rules  of  the  Road,  both  Inter- 
national and  Inland,  should  be  carried  on  with  Chapter  7; 
and  the  letter  of  the  rules  thoroughly  mastered,  the  Inland 
Rules  are  commonly  known  as  the  blue  book,  while  the  In- 
ternational are  in  Department  Circular,  No.  230,  Depart- 
ment of  Commerce. 

359891 


NOTE. 

In  correcting  the  observed  altitude  a  good  alti- 
titude  correction  table  may  be  used  in  practice.  In 
the  1914  edition  of  Bowditch,  Table  46  for  this  pur- 
pose has  been  added;  enter  it  with  the  height  of  the 
eye  at  the  top  and  altitude  at  the  side,  the  desired 
correction  for  sun  or  star  is  found  at  intersecting 
point;  additional  correction  found  at  bottom  of  page 
to  allow  for  change  in  semi-diameter. 

If  the  navigator  uses  the  American  Nautical 
Almanac  he  will  not  now  (1916)  need  to  correct  the 
declination  or  equation  of  time;  they  are  given  for 
every  two  hours  of  each  day,  and  values  for  inter- 
mediate hours  may  easily  be  obtained  by  interpola- 
tion. 

Use  Bowditch  in  conjunction  with  this  book  for 
the  tables  referred  to. 


(4) 


CHAPTER  ONE. 


Article  i  (a)     Middle  Latitude  Sailing. 


Case 

Given 

To  Find 

Solution 

1 

Both 
Lats.  & 
Longs. 

Dep. 
Course 
Dist. 

Dep.  = 
Tan.  C  = 
Dist.  = 

D.Lo.  x 
Dep.     -r 
Sec.  C.  x 

Cos.  M.  L. 
D.L. 
D.L. 

2 

Both 
Lat. 
&  Dep. 

Course 
Dist. 
D.Lo. 

Tan.  C  = 
Dist.  = 
D.Lo.  = 

Dep.     - 
Dep.     - 
Dep.     - 

D.L. 

Sin.  C. 
Cos.  M.  L. 

3 

One 
Lat.  C. 
&  Dist. 

D.  L. 
Dep. 
D.Lo. 

D.L.  = 
Dep.  = 
D.Lo.  = 

Dist.     x 
Dist.     x 
Dep.      x 

Cos.C. 
Sin.  C. 
Sec.  M.  L. 

4 

Both 
Lats. 
&  C. 

Dep. 
Dist. 
D.Lo. 

Dep.  = 
Dist.  = 
D.Lo.  = 

D.'L.     x 

D.L.     -=- 
Dep.      x 

Tan.  C. 
Cos.  C. 
Sec.  M.  L. 

5 

Both 
Lats.  & 
Dist. 

C. 
Dep. 
D.Lo. 

Cos.C.  = 
Dep.  = 
D.Lo.  = 

D.L.     - 
Dist.     x 
Dep.      x 

Dist. 
Sin.  C. 
Sec.  M.  L. 

6 

One 
Lat.  C. 
&Dep. 

D.L. 
Dist. 
D.Lo. 

D.L.  = 
Dist.  = 
D.Lo.  = 

Dep.      -=- 
Dep.      -:- 
Dep.      x 

Tan.  C. 
Sin.  C. 
Sec.  M.  L. 

(5) 


Article  i  (b)          Mercator  Sailing. 


Case 

Given 

To  Find 

Solution 

1 

Both 
Lats.  & 
Longs. 

C. 
Dist. 
Dep. 

Tan.C.  = 
Dist.     = 
Dep.     = 

D.Lo.  - 

Sec.C.  x 
D.L.  x 

m. 
D.L. 
Tan.  C. 

2 

Both 
Lats.  & 
Dep. 

C. 
Dist. 
D.Lo. 

Tan.C.  = 
Dist.      = 
D.Lo.    = 

Dep.  -f 
D.L.  x 
m. 

D.L. 
Sec.  C. 
Tan.  C. 

3 

One 
Lat.C. 
&  Dist. 

Dep. 
D.L. 
D.  Lo. 

Dep.     = 
D.L.     = 
D.Lo.    = 

Dist.  x 
Dist.  x 
m. 

Sin.  C. 
Cos.  C. 
Tan.  C. 

.4 

Both 
Lats. 
&  C. 

Dist. 
Dep. 
D.Lo. 

Dist.     = 
Dep.     = 
D.Lo.    = 

D.L.  - 
D.L.  x 
m. 

Cos.  C. 
Tan.  C. 
Tan.  C. 

5 

Both 
Lat.  & 
Dist. 

C. 
Dep. 
D.Lo. 

Cos.C.  = 
Dep.     = 
D.Lo.    = 

D.L.  - 

Dist.  x 
m. 

Dist. 
Sin.  C. 
Tan.  C. 

6 

One 
Lat.  C. 
&  Dep. 

D.L. 
Dist. 
D.Lo. 

D.L.     = 
Dist.     = 
D.Lo.    = 

Dep.  -f- 
Dep.  - 
m. 

Tan.  C. 
Sin.  C. 
Tan.  C. 

(6) 


Note.  To  use  any  formula  in  these  sailings  find  the  ease 
it  is  necessary  to  use  by  an  examination  of  what  is  given  and 
what  it  is  desired  to  find,  then  do  the  work  according  to 
the  form  in  Chapter  1,  Article  2.  To  analyze  a  formula  take 
for  instance  Case.  2,  Mid.  Lat.  Sailing;  it  is  readily  seen 
that  both  Latitudes  and  Dep.  are  given  to  find  the  Course, 
Dist.  and  D.  Lo. ;  obviously  then  the  first  unknown  quantity 
is  the  Course;  following  along  to  the  Solution  there  is 
found  Tan.  C.  =  Dep.  ~  D.  L.,  i.  e.  the  log.  of  the  D.  L.  sub- 
tracted from  the  log.  of  the  Dep.  will  leave  the  log.  tangent 
of  the  true  course  (T.  C.) ;  so  in  the  work  form  write  in  the 
Dep.  and  D.  L.  and  pick  out  their  logs ;  subtract  them  and 
the  result  is  a  tangent  which  being  found  in  Table  44  will 
give  the  T.  C.  An  explanation  of  one  formula  will  apply  to 
any  used  in  this  work;  the  only  point  to  remember  is  that 
the  sign  x  means  add,  and  the  sign  -f-  means  subtract. 


(7) 


Article  2. 


DAY'S  WORK. 


Work  Form  Mercator's  Sailing1. 


Comp.  Courses 

Var. 

Dev. 

Error 

True  Courses 

Dist. 

N 

S 

E 

W 







— 

Lat.  Left                          Merid.  parts 
D.  L. 

Lat.  in 

u           u 

m. 

SOLUTION. 

Dep. 

log. 

D.L. 

log.                    log. 

T.  C. 

Tan.                   Sec. 

Tan. 

Dist. 

Log. 

m. 

Log. 

D.  Lo. 

Log. 

Long,  left 

D.  Lo. 

Long,  in 

Middle  Latitude  Sailing. 


Work  Form. 
Traverse  Table  as  per  Chapter  1,    Article  2. 


Lat.  left 
D.  L. 
Lat.   in 
£D.  L. 
Mid.  Lat. 


(N.  or  S.) 


(Add  to  lesser  Lat.,  or  subtract 

from  greater  Lat.) 


(8) 


Use  solution  according  to  case  required  and  work  form, 
Chapter  1,  Art.  2. 


The  work  forms  in  this  Article  may  be  used  for  any  case 
by  changing  the  data  in  the  Solution  to  meet  the  require- 
ments. 


For  Turning  Compass  Points  into  Degrees. 


Points 

Degrees. 

Points 

Degrees 

0 

/ 

" 

0 

' 

rr 

Y± 

2 

48 

45 

4M 

47 

48 

45 

Yi 

5 

37 

30 

4)| 

50 

37 

30 

% 

8 

26 

15 

4% 

53 

26 

15 

i 

11 

15 

00 

5 

56 

15 

00 

1% 

14 

03 

45 

5/4 

59 

03 

45 

iK 

16 

52 

30 

5K 

61 

52 

30 

1% 

19 

41 

15 

5% 

64 

41 

15 

2 

22 

30 

00 

6 

67 

30 

00 

2/4 

25 

18 

45 

6J4 

70 

18 

45 

01  / 

/z 

28 

07 

30 

6/4 

73 

07 

30 

2^ 

30 

56 

15 

6% 

75 

56 

15 

3 

33 

45 

00 

7 

78 

45 

00 

3/i 

36 

33 

45 

7M 

81 

33 

45 

slA 

39 

22 

30 

7M 

84 

22 

30 

3% 

42 

11 

15 

7% 

87 

11 

15 

4 

45 

00 

00 

8 

90 

00 

00 

(9) 


Day's  Work  Described. 


Art.  3.  Correct  each  course  for  leeway,  if  any,  turn  the 
result  into  degrees,  min.,  and  sec.  by  means  of  Table  in  Art.  2 
always  counting  number  of  points  from  N.  or  S.  towards  E. 
or  W. 

Example. 

Course  S.  S.  W.  y2  W.  =  2y2  points  found  in  the  table 
to  equal  28°  7'  30";  turn  min.  and  sec.  into  tenths  (decimal) 
of  a  degree,  thus :  — 

Divide  30"  by  60.  6  )     30 

Result,   decimal  of  a  min.  .5 
The  min.  then  are            7.5 

Which  divide  by  60,       result  6  )     7.5 


Decimal  of  a  degree  .12 

Course  ready  to  use  is  S.  28.1°  W.  If  .second  decimal 
place  is  over  5,  use  next  highest  tenth,  rejecting  second  figure. 
This  method  of  dividing  by  60  is  to  reject  the  cipher  and 
point  off  one  more  place,  and  may  be  used  as  short  method 
either  in  arc  or  in  time. 

Enter  course,  in  above  form,  in  column  marked  Comp, 
Courses,  with  Var.  and  Dev.  abreast  in  their  respective  col- 
umns. Deduce  the  error,  enter  it  and  apply  to  the  comp. 
course  —  to  the  left  if  West,  to  the  right  if  East,  determined 
by  standing  in  the  center  of  the  compass,  in  imagination,  and 
facing  towards  the  rim  in  the  direction  of  the  course  —  en- 
tering the  resulting  true  course  (T.  C.)  with  the  distance 
sailed.  When  all  courses  are  entered,  Dep.  first  and  Current 
last,  start  at  the  top  and  enter  Table  2,  finding  the  degrees 
up  to  45  at  the  top  of  the  page,  thence  to  90°  at  the  bottom. 
Find  the  distance  in  col.  of  dist.,  and  opposite  will  be  the 
Dif.  of  Lat.  (D.  L.)  and  Departure  (Dep.)  in  their  respective 
columns,  taking  their  names  from  top  or  bottom  of  col., 
according  as  the  degrees  are  found  at  top  or  bottom. 

(10) 


Example. 

Suppose  a  course  S.  57.6°  E.     Dist.  50  miles. 

Enter  Table  2  degrees  at  bottom,  so  cols,  will  be  named 
from  bottom. 

D.  L.  Dep. 

27.2  57°  41.9 

26.5  58  42.4 

.7  .5 

these  differences  are  for  1°  or  ten-tenths;  one-tenth  will 
equal  a  division  by  10,  and  for  the  required  dif .  or  .6,  multiply 
by  6,  thus :  — 

.07     =     dif.   for  one-tenth 

_6 

.42  six-tenths 

and 

.05     =     dif.  for  one-tenth 

_6 

.30     =  six-tenths 

An  examination  of  the  D.  L.  shows  that  it  is  decreasing 
from  57°  to  58°,  consequently  the  cor.  of  .4  is  subtracted 
from  27.2  =  26.8  the  D.  L.  for  57°. 6  course. 

Dep.  is  seen  to  be  increasing  so  the  cor.  of  .3  is  to  be 
added  to  41.9  =  42.2  the  Dep.  for  this  course. 

Enter  D.  L.  and  Dep.  in  traverse  table,  taking  care  to 
observe  the  direction  sailed.  When  all  the  courses  have  been 
handled  in  this  manner,  add  up  the  N.  S.  E.  and  W.  cols., 
subtract  the  lesser  D.  L.  from  the  greater  and  the  lesser 
Dep.  from  the  greater,  and  the  result  is  the  D.  L.  (N.  or  S.) 
and  Dep.  (E.  or  W.)  which  has  been  made. 

Place  D.  L.  under  Lat.  left,  first  turning  it  into  degrees 
and  minutes  if  it  is  60'  or  over,  and  name  it  N.  or  S.  as 
the  case  may  be,  also  name  Lat.  left;  if  they  are  of  unlike 
names,  subtract ;  like  names,  add ;  result,  Lat.  in. 

If  it  is  desired  to  work  in  Mid.  Lat.  Sailing,  divide  D.  L. 
by  2,  placing  result  under  Lat.  in,  and  either  add  it  to  the 
smaller,  or  subtract  from  the  greater,  of  the  two  Lats. 

(11) 


If  it  is  desired  to  work  in  Mercator's  Sailing,  turn  to 
Table  3,  and  pick  out  the  Meridianal  Parts  for  each  Lat. ; 
if  both  Lats.  are  on  the  same  side  of  the  Equator,  subtract ; 
different  sides,  add ;  result,  Meridianal  D.  L.  or  m.  Follow 
the  formula  in  Case  2,  Mercator's  Sailing,  Chap  1,  Art.  1  (b). 
Fill  in  Dep.  and  D.  L.  in  Work  Form;  pick  out  their  logs 
from  Table  42,  subtracting  log  of  D.  L.  from  log  of  Dep. 
and  the  resulting  log  will  be  the  tangent  of  the  true  course 
(T.  C.)  ;  find  this  tan.  in  Table  44  and  fill  in  T.  C.,  taking  the 
degrees  from  the  top  or  bottom  of  the  page,  according  as 
the  name  of  tan.  col.  was  taken  from  top  or  bottom.  Find  the 
sec.  at  same  time  and  place  abreast  the  tan.  and  again  carry 
out  tan.  in  line  with  sec. ;  over  the  sec.,  write  in  log  of  D.  L. ; 
the  sum  of  these  two  logs  will  be  the  log  of  the  dist.  which 
find  in  Table  42.  Fill  in  m  in  Work  Form  and  find  its  log 
in  Table  42  which  add  to  tan.  of  T.  C. ;  result  log  of  D.  Lo. 

If  the  dist.  run  is  short,  or  does  not  include  much  change 
in  Lat.  the  Mid.  Lat.  sailing  will  be  equally  as  good  and 
may  be  done  by  inspection  as  follows :  - 

Enter  Table  2  with  Mid.  Lat.  as  a  course,  find  Dep.  in 
col.  of  D.  L.  and  opposite  in  col.  of  dist.  will  be  the  D.  Lo. ; 
in  Table  2,  find  that  place  where  D.  L.  and  Dep.  most  nearly 
correspond,  opposite  col.  of  dist.  will  be  the  Dist.  and  the 
T.  C.  will  be  found  (degrees  at  top  or  bottom)  according  as 
D.  L.  and  Dep.  cols,  are  named  from  top  or  bottom.  Place 
D.  Lo.  under  Long,  left  by  turning  it  into  degrees  and  min- 
utes if  60'  or  over,  name  it  E.  or  W.  in  accordance  with  name 
of  Dep.  and  having  named  Long,  left,  combine  the  two ;  like 
names  add,  unlike  names  subtract;  resulting  Long,  to  take 
name  of  the  greater.  It  may  be  remarked  that  any  of  the 
Sailings  may  be  worked  by  inspection. 

Note.  Dep.  course  is  first  and  is  corrected  for  Var.  and 
Dev.  current  course  is  last  and  is  corrected  for  Var.  only. 
To  find  a  departure  course,  observe  the  bearing  of  a  light  or 
fixed  point,  correct  this  bearing  and  reverse  it. 


(12) 


Article  3. 

Position    by   Bearings. 


MAKING  A  LIGHT. 

The  officer  of  the  deck,  knowing  he  will  make  the  land 
in  his  watch,  has  Kis  list  of  lights  handy,  in  order  to  obtain 
the  visibility,  and  knowing  the  height  of  his  eye  above  the 
sea  in  the  location  where  his  watch  is  to  be  stood,  picks  out 
beforehand,  from  Table  14,  Bowditch,  the  correction  for  dip. 
Suppose  he  is  running  towards  Boston  and  expects  to  make 
Highland  Light;  as  soon  as  it  appears  clearly  above  the 
horizon,  he  takes  a  careful  bearing  across  the  compass,  or 
better  still  with  a  pelorus,  if  he  has  one  at  hand,  looks  up 
the  visibility  in  the  light  book  and  corrects  it  for  dip,  of 
course  adding  the  correction  because  the  visibility  is  given 
for  the  sea  level  and  the  ship's  bridge  may  be  forty  feet 
above.  Correct  the  obs.  bearing  for  the  Dev.  of  the  com- 
pass on  the  course  steered  and  lay  it  down  on  the  chart; 
measure  the  dist.  of  visibility  plus  the  cor.  for  dip  from  the 
light  and  where  this  cuts  the  line  of  bearing  is  the  position  of 
the  ship.  Being  liable  to  error  on  account  of  refraction,  this 
method  is  only  a  check  and  is  not  considered  reliable ;  but 
in  case  it  should  shut  in  thick  shortly  afterwards,  it  would 
ease  the  "old  Man's"  mind  a  little  if  the  officer  of  the  deck 
could  give  him  the  "Fix." 


Light.  _ 


(13) 


FOUR  POINT  BEARING. 

When  the  Highlands  bears  four  points  on  the  bow,  note 
the  time  carefully,  also  the  log  if  the  speed  is  not  accurately 
known,  and  hold  the  same  course  till  the  light  is  abeam.-, 
the  distance  run  between  the  bearings  is  the  distance  off  at 
the  time  of  the  beam  bearing.  Here  also  error  may  creep 
in,  owing  to  tide  or  carelessness,  the  latter  should  not  be, 
and  the  former  may  generally  be  judged  fairly.  If  this  po- 
sition jibes  with  the  first  one  and  falls  on  the  track,  the  officer 
may  feel  quite  secure  and  is  justified  in  the  belief  that  he  will 
make  the  Light-Ship  about  as  he  has  figured.  If  he  feels  any 
doubt  however,  about  his  bearing  being  good.,  again  note  the 
time,  when  it  is  four  points  abaft  the  beam,  and  another 
check  is  established.  In  coasting  where  the  lights  are  not 
too  far  apart,  the  speed  over  the  bottom  can  be  quite  accu- 
rately established  by  dividing  the  total  number  of  minutes 
between  two  lights  by  the  distance,  establishing  the  number 
of  minutes  it  takes  to  run  one  mile ;  hence  the  distance  off 
is  found  and  is  not  apt  to  be  much  affected  by  tide  under 
ordinary  conditions.  Of  course  if  it  is  bad  weather  and  the 
speed  of  the  ship  irregular  and  uncertain,  this  is  not  reliable. 
A  point  to  be  thought  of  is  that  a  poor  four  point  bearing 
is  worse  than  none  because  it  may  give  confidence  in  a  false 
position.  The  careful  navigator,  however,  is  ever  alert  to 
the  possibility  of  mistakes,  and  it  is  well  for  the  young  of- 
ficer to  remember  that  the  over  confident  man  may  come  to 
grief  through  neglecting  to  use  some  one,  or  all  of  these 
opportunities  to  place  his  ship. 


Light. 


(14) 


CROSS  BEARINGS. 

Once  more  may  the  position  be  obtained  using  the  High- 
lands as  a  factor,  provided  the  ship  is  far  enough  to  the 
Southward  to  see  The  Race.  If  it  is  made,  the  officer  of  the 
deck  immediately  takes  a  bearing  on  it  and  as  quickly  as 
possible  swings  the  sight  vanes  round  to  bear  on  the  High- 
lands. Correct  these  bearings  for  the  Dev.  for  course  steered 
and  plot  them  on  the  chart ;  the  point  of  intersection  is  of 
course  the  position  of  the  ship.  Take  careful  bearings  and 
if  the  Dev.  is  known,  this  method  is  very  reliable  if  the 
angle  is  good ;  as  nearly  as  possible  to  90°  is  the  best  angle 
for  cross  bearings,  but  never  less  than  30°,  nor  more  than 
150°. 

If  the  pelorus  is  used,  set  it  for  the  magnetic  head  of  the 
ship  and  the. bearings  will  then  not  need  correcting;  also 
be  particular  that  the  ship  is  steady  on  her  course.  In  using 
cross  bearings,  a  third  one  may  be  used  with  these  two  if  it 
comes  inside  the  limits. 


Eace  Point.     ~ -^ 


Highlands.  _ 


(15) 


BY  TWO  BEARINGS. 

A  handy  thing  to  remember  is  that  if  a  bearing  of  a 
light  is  taken  26^°  on  the  bow  and  again  45°  on  the  bow, 
the  run  between  these  bearings  will  be  the  distance  off  the 
light  when  abeam.  Try  this  in,  conjunction  with  the  Four 
Point  Bearing.  It  is  a  good  thing  to  use  if  there  are  outlying 
dangers  off  this  light  for  the  navigator  must  assure  himself 
beforehand  that  he  is  going  to  pass  far  enough  off.  There  are 
other  methods  that  are  good  if  convenient  tables  are  at 
hand,  such  as  the  Danger  Angle  taken  with  a  sextant,  any 
two  bearings,  etc.,  but  it  is  not  the  purpose  of  the  author  to 
make  this  work  cumbersome  and  these  methods  are  easily 
learned  in  Bowditch  or  Lecky. 


Shoals. 


Bearing  taken  at  A 
261/2°  on  the  bow,  again 
at  D  45°  on  the  bow ;  dist. 
sailed  A  D  =  B  C :  or  the 
dist.  the  vessel  will  be  off 
at  C  is  known  at  the  point 
D. 


(16) 


CHAPTER  II. 


Latitude. 

Article  l.  Meridian  Altitude  of  Sun    (0) 

Work  Form. 

h.  m.  s.  hrs. 


Obs.  Alt. 
Cor. 

Long. 

(N.orS.)  H.  D. 
Hrs. 

h. 
90 

Ap.Dec.  . 

Cor. 
Cor.Dec. 

(N.orS.)  Cor. 

Dip.  -                S.D.  + 
Ref.   -                Par   + 

M.Z.D. 
Cor.Dec. 

(N.orS.) 
(N.orS.) 

Lat. 

(N.orS.) 

Cor.     + 

To  have  work  ready  for  noon,   use  the  following  :  — 
Case  I.     Lat.  and  Dec.  same- name,  Lat.  the  greater 

'  +90°  +  Dec.  -  Cor.  -  Obs.  Alt. 
Case  II.      Lat.  and  Dec.  same  name,  Djec.  the  greater 

-90  +  Dec.  +  Cor.  +  Obs.  Alt. 
Case  III.      Lat.  and  Dec.  opposite  names. 
+  90  -  Dec.  -  Cor.  -  Obs.  Alt. 

Case  I.                    Case  II.  Case  III. 

+90°  00'  00"  -90°  00'  00"  +90°  00'  00" 

Dec.  +23  27  22  +9     14    11  -18     50    49 

Cor.  13  21  +           8   59  12      2 

Constant    +113  14     1  -80    36  50  +70     57      9 

Obs.  Alt.        -40       4    0  +81     15  30  -30    13    10 

Lat.                  73  10     IN.           0     38  40 N.  40    43    59 S 

(17) 


Observe  the  lower  limb  of  the  sun  in  contact  with  the 
horizon,  and  apply  the  I.  C.  if  any ;   result,  Obs.  Alt. 
Turn  the  Long,  into  hours  and  decimal  thus:  — 
Long.  70°  15'  30"  divide  by  15. 
15  in  70  =  4  hrs.,  'with  a  remainder  of  10°  = 
600  +  15'  =  615  -j- 15  =  41  min.   30 -f  15  =  2 
Result  Long,  in  time,  4  h.  41  m.  2  s.  on  the  principle  that 
1  hour  =  15°.     Divide  sec.  and  min.  by  60  by  short  method 
of  dropping  the  cipher  and  point  off  one  extra  place. 

6  )  2 
6  )  41.03 


.68 

As  8  is  more  than  5,  reject  it  and  call  the  tenths  (.7) 
Long,  in  time  =  4.7  hrs. 

In  practice,  this  part  can  be  done  in  the  head,  and  fill 
in  the  Work  Form.  Enter  Page  1  of  American  Nautical 
Almanac  for  the  date  and  pick  out  Ap.  Dec.  with  its  hourly 
dif.  (H.  D.)  and  the  semi-diameter  (S.  D.)  Multiply  H.  D. 
by  the  hrs.  (or  Long,  in  time)  applying  result  to  Ap.  Dec. 
as  Cor.  according  to  this  rule :  In  W.  Long.,  if  Dec.  is  in- 
creasing, add ;  decreasing,  subtract ;  in  East  Long.,  vice- 
versa.  Be  particular  to  name  the  Dec. 

Enter  Table  14  of  Bowditch  and  pick  out  Cor.  for  height 
of  eye,  or  dip.  In  Table  20  A  find  ref.,  and  in  Table  16  Par. 
Fill  these  in  the  Work  Form  and  the  total  Cor.  will  be  found 
to  be  additive ;  apply  it  to  Obs.  Alt. ;  result  C.  C.  A.  or  h. 
Subtract  h.  from  90°  to  find  M.  Z.  D.  (Meridian  Zenith  Dis- 
tance) or  in  other  words  the  dist.  the  sun  is  from  the  ob- 
server 's  zenith  when  on  the  meridian,  and  it  is  named  opposite 
to  the  sun's  bearing.  Place  Dec.  under  M.  Z.  D.  and  apply 
as  follows:  — Like  names,  add;  unlike  names,  subtract. 
Result  is  the  Lat.,  taking  the  name  of  the  greater. 

Note.  —  When  the  navigator  works  his  morning  sight 
and  carries  his  position  forward  to  noon  the  long,  is  suf- 
ficiently accurate  to  correct  the  dec.  The  Lat.  is  generally 
known  to  be  either  N.  or  S.  and  the  obs.  alt.  will  be  known 
near  enough  to  find  the  ref.  and  par. ;  hence  the  correction 
for  the  obs.  alt.  can  be  quite  accurately  figured  beforehand ; 
and  all  he  needs  to  do  is  to  see  which  case  applies  and  work 
it  up  as  far  as  the  "Constant,77  when  he  is  ready  to  apply 
his  obs.  alt.  and  give  the  Lat.  to  the  captain  promptly  at 
eight  bells.  (See  Case  I,  II  and  III  at  end  of  Work  Form.) 

(18) 


Article  2. 


Ex-Meridian  Alt.  of  Sun. 


Work  Form. 


Watch 
C.-W. 

Ap.  Dec. 
Cor. 

H.D. 
Hrs. 

Chro. 
Cor. 

Cor.  Dec. 

H.D. 
Hrs. 

G.  M.  T. 

Eq.  T. 

Eq.T. 
Cor. 

G.Ap.T. 
Long. 

Cor.  Eq.T. 
=hrs. 

Dip.- 
Eef.- 

S.  D.+ 
Par.   + 

L.  Ap.T. 

12 


Obs.  Alt. 

Cor.+  

h. 

at2+      

H. 

90 


Cor.  + 

(Table  26)a   = 
(     «      27)at2= 


z. 

d. 

Lat. 

(at  time  of  sight) 
D.  L.  to  noon 
Noon   Lat. 


The  use  of  Tables  26  and  27  in  Bowditch  is  confined  to 
an  intervalfrom  noon  not  greater  than  26  min.  though  this 
problem  may  be  worked  reliably  at  a  greater  interval  with 
other  tables  if  at  hand.  This  explanation,  however,  is  that 
of  the  Bowditch  method. 


(19) 


Care  must  be  used  in  observing  the  alt.  that  the  time  is 
accurately  noted  on  the  watch,  from  which  find  chro.  time 
by  applying  C-W  and  the  chro.  error  applied  will  give  G.  M. 
T. ;  to  this  apply  the  Cor.  Eq.  T.  from  page  1  of  the  Almanac ; 
result  G.  Ap.  T.  To  this  apply  the  Long,  in  time,  subtract- 
ing if  W.  and  the  result  is  Local  Apparent  Time  (L.  Ap.  T.) 
which  subtracted  from  12  hours  will  give  the  interval  from 
noon,  marked  t,  if  L.  Ap.  T.  is  A.  M. ;  if  it  is  P.  M.,  it  will 
not  be  necessary  to  subtract  from  12  hours  as  the  time  itself 
will  equal  t.  Using  the  Work  Form  find  the  Ap.  Dec.  in  page 
1  of  the  Almanac  and  take  H.  D.  at  same  time,  also  Eq.  T. 
and  its  H.  D.  Correct  the  Dec.  and  Eq.  T.  for  Long,  as  al- 
ready described  in  Chap.  II,  Art.  1.  Correct  the  Alt.,  finding 
value  of  h.  Enter  Table  26  with  Dec.  at  top  and  Lat.  at 
side,  paying  attention  to  their  names,  and  at  their  junction 
will  be  a  cor.  in  seconds  which  is  =  to  a  in  Form ;  this  is  the 
variation  in  alt.  in  one  min.  from  noon.  Enter  Table  27  with 
"t"  at  the  top  and  "a"  at  the  side  and  at  their  junction  will 
be  found  at2  or  the  correction  to  be  applied  +  to  the  cor.  alt. 
(h)  to  find  the  value  of  H. ;  or  in  other  words  H.  is  the  merid. 
alt.  for  the  meridian  on  at  time  of  sight.  The  Lat.  is  then 
found  by  applying  H.  to  90°,  etc.,  as  explained  in  Chap.  II, 
Art.  1.  It  must  be  remembered  however,  that  this  Lat.  is 
for  a  time  from  noon  equal  to  the  value  of  "t"  during  which 
interval  probably  the  ship  has  not  been  standing  still,  con- 
sequently the  D.  L.  made  must  be  applied  in  order  to  have  the 
correct  Lat.  at  Noon.  This  D.  L.  is  readily  found  by  in- 
spection in  Table  2  as  explained  in  Chapter  1,  Art.  2. 


(20) 


Article  3.         By  Mer.  Alt.  of  Fixed  Star. 

Work  Form. 

G.  M.  T.  Merid.  Passage  Dec. 

C.-W.  

Watch  Dip.- 

Ref.-_ 

Cor.- 


Obs.  Alt. 

Cor. 

L 


90 


z.  (N.  or  S.) 

d. (N.  or  S.) 

Lat.  (N.  or  S.) 

From  the  table  in  Am.  Nautical  Almanac  Supplement, 
find  the  time  of  merid.  passage  of  the  star,  also  its  Dec.  from 
table  of  Apparent  Places.  Compare  the  watch  with  G.  M.  T. 
and  note  the  altitude  at  the  moment  of  transit  by  the  watch. 
Correct  the  Alt.  for  I.  C.  if  any,  to  find  the  Obs.  Alt.  The 
cor.  for  Dip.  and  Ref.  are  to  be  taken  from  Tables  14  and 
20  A.  Apply  this  total  cor.  (always  minus)  to  the  Obs.  Alt. 
From  this  point  proceed  as  in  Chap.  II,  Art.  1.  In  taking  the 
Dec.  from  the  Almanac  sign  +  means  North,  and  sign  — 
means  South.  Care  should  be  used  in  stellar  observations 
to  select  a  star  whose  merid.  passage  occurs  in  as  good  day- 
light as  may  be  to  enable  the  observer  to  see  the  horizon  most 
distinctly,  which  cannot  always  be  done  except  with  Polaris. 
Frequently  a  star  can  be  had  in  the  North  and  one  in  the 
South  at  the  same  time.  If  the  merid.  passage  does  not  occur 
just  right,  make  an  Ex-Meridian  of  it  just  the  same  as  with 
the  sun.  If  taking  a  morning  sight,  begin  before  daylight 
and  bring  the  star  down  to  the  horizon  while  it  is  bright 
enough  to  do  so  easily;  watch  it  every  few  minutes  as  it 
comes  daylight,  or  until  the  moment  of  merid.  passage;  or 

(21) 


figure  up  the  Lat.  by  D.  R.  and  from  this  work  backward  to 
the  alt.  and  set  the  sextant ;  unless  quite  an  error  has  been 
made,  the  star  may  easily  be  found  this  way.  This  latter 
method  is  generally  used  in  the  evening  twilight  when  it  is 
desirable  to  observe  the  alt.  as  early  as  possible,  or  before 
the  horizon  grows  indistinct.  The  alt.  of  a  star  is  only  cor- 
rected for  Dip.  and  Ref .  Obviously  Semi-Diameter  and  Paral- 
lax would  be  so  small  as  not  to  be  practical  in  any  naviga- 
tional work. 

Note.     In  all  altitude  corrections,  see  note  in  front  of 
book  for  use  of  Table  46,  1914  edition  of  Bowditch. 


Article  4.  By  Polaris  (North  Star). 

Work  Form. 

Dip. 

L.  M.  Ast.  T.  Ref. 

Red.  Table  III  Cor.~ 

G.  Sid.  T. 

Red.  Table  III Obs.  Alt. 

L.  Sid.  T.  Cor.  

True  Alt. 

H.  A.  Cor. 

Lat. 


This  form  is  for  the  method  described  in  the  back  of  the 
American  Nautical  Almanac  which  is  given  so  clearly  that 
it  is  not  deemed  necessary  to  repeat  it  here.  The  tables  for 
all  corrections  are  given  in  the  same  part  of  the  book.  This 
method  is  sufficiently  accurate  for  navigational  purposes  and 
is  shorter  than  that  given  in  Bowditch. 

(22) 


CHAPTER     III. 


Longitude. 


Article  1                          Time  Sight. 

Hrs.  Min.  Sec. 
Watch                                   Ap.  Dec. 
C.-W.                                    Cor. 

H.D. 
Hrs. 

Cor. 

Chro. 
Error 

Cor.  Dec. 
P.  D.            90 

G.  M.  T. 

*                   12 

Eq.  T. 

Cor. 

H.D. 
Hrs. 

G.  M.  A.  T. 
24 

Before  noon. 

Obs.  Alt. 
Cor.  + 

Hrs.     Cor.  Eq.  T. 
Dip.- 
Ref.- 

Cor. 
S.D.+ 
Par.+ 

- 

t 

h. 
Lat. 
P.  D. 

Sec. 
Cosec. 

Cor.+ 

S.        2) 

IS. 

h. 

Cos. 

Rem. 

Sin, 

(23) 


L.  Ap.T.  Sin. 

Eq.  T. 
L.  M.  T.  ~ 
*  12 

L.M.A.T." 
G.M.A.T._ 
Long,  in  time 

15 


Long.  E.  orW. 

D.  Lo.       E.  orW.  Table  38 

Noon  Long.  E.  orW.  Cor.  for 

Lat.  error 

A  M  run;  T.  C.  Dist. 

Mid.  Lat.  D.  L.  Dep.  D.Lo. 


Compare  the  watch  with  chro.  finding  the  watch  error 
on  G.  M.  T.  (Greenwich  Mean  Time),  then  when  the  sun  is 
as  near  the  prime  vertical  as  possible,  or  its  azimuth  is  nearest 
to  90°,  but  so  the  altitude  will  be  more  than  6°,  take  an  alt. 
of  O  noting  the  time  carefully  on  the  watch ;  a  good  way 
being  to  begin  the  moment  the  alt.  is  taken  and  count  thus : 
1  and  2  and  3  and  4  and  5  —  meantime,  lowering  the  sextant 
and  removing  the  watch  from  the  pocket  you  are  ready  to 
note  the  seconds  by  the  time  you  have  counted  5  in  this 
manner,  deducting  5  s.  from  the  number  noted;  it  is  then 
an  easy  matter  to  note  the  min.  The  old-fashioned  deep 
water  method  of  having  a  boy  or  two  stationed  along  on 
deck  to  sing  out  Time,  perhaps  with  the  mate  taking  the 
sight  from  forward  somewhere  if  she  happens  to  be  heading 
to  the  Eastward,  meant  a  possible  error  of  four  or  five  seconds 
by  the  time  the  word  reached  the  "old  man"  in  the  cabin 
noting  the  chro.,  and  is  impossible  in  a  modern  steamer,  ac- 
curacy being  the  key  note  of  up-to-date  navigation.  If  more 
than  one  sight  is  to  be  taken,  though  one  good  one  is  as  good 

*   If  time  is  P.  M.,     leave    out   this    operation     as   it   will    already  be 
Astronomical  Time. 

(24) 


as  a  dozen,  read  off  your  alt.  as  quickly  as  possible  and  note 
it  with  the  time ;  bring  the  sun  down  again,  and  repeat  the 
same  operation.  Sometimes  two  sights  are  taken  and  used 
as  in  a  Sumner;  and  again  three  sights  and  the  mean  of 
them  and  of  the  times  is  used  although  it  is  rather  out  of 
date  to  do  so.  Now  prepare  the  data.  To  the  watch  time 
apply  C-W.  then  the  Chro.  Error  and  the  result  is  G.  M.  T. ; 
if  between  midnight  and  noon,  add  12  to  the  hours  and  sub- 
tract 1  from  the  date  which  reduces  it  to  G.  M.  Astronomical 
T. ;  if  it  falls  after  noon,  this  calculation  is  unnecessary  as 
G.  M.  T.  is  already  Astronomical  Time  and  it  is  also  the  time 
from  noon  with  which  to  correct  Dec.  and  Eq.  T.  If  before 
noon,  subtract  it  from  24  to  find  the  interval  from  noon. 
Turn  this  interval  into  hours  and  decimals  of  an  hour  as  ex- 
plained in  Chap.  II,  Art.  1. 

Enter  Page  II  of  the  Almanac  for  the  nearest  noon  and 
pick  out  the  Dec.  and  Eq.  of  Time  with  their  H.  D.'s  which 
multiply  by  the  interval  from  Noon.  Apply  these  cor.  ac- 
cording as  the  Dec.  and  Eq.  of  T.  are  increasing  or  decreas- 
ing and  whether  the  time  interval  is  before  or  after  noon. 
Notice  at  top  of  Eq.  of  T.  col.  how  it  is  to  be  applied  to  Ap. 
T.  which  will  be  found  to  be  opposite  to  the  way  it  is  ap- 
plied to  mean  time,  and  place  the  proper  sign  before  it  in 
order  to  know  what  to  do  with  it  when  the  proper  time 
comes  to  use  it.  Find  the  Polar  Dist.  (p.)  which  is  the  dist. 
the  sun  is  from  the  observer's  nearest  pole,  by  applying  the 
Dec.  to  90°,  according  to  the  following  rule:  Lat.  and  Dec. 
same  name,  subtract;  different  names,  add.  Correct  the 
obs.  alt.  for  Dip,  Eel,  S.  D.  &  Par.,  and  mark  it  h.  Add 
together  h.  +  Lat.  +  p.,  take  the  half  sum  and  subtract  h. 
Enter  Table  44,  find  the  secant  of  the  Lat.  cosecant  of  p., 
cosine  of  %  S.  and  sine  of  Hem.  Half  the  sum  of  these  four 
logs  will  be  the  sine  of  the  Hour  Angle  or  L.  Ap.  T.  taken 
from  A.  M.  pr.  P.  M.  col  of  Table  44,  according  as  the  time 
of  sight  was  A.  M.  or  P.  M.  Apply  Eq.  of  T.  and  if  the  re- 
sulting L.  M.  T.  is  before  noon,  turn  it  into  astronomical 
time  by  adding  12  to  the  hours,  and  it  is  a  matter  of  course 
that  whenever  this  is  done  and  the  date  is  needed  to  be  used, 
subtract  one  from  it.  Bring  down  G.  M.  A.  T.  and  subtract 

(25) 


the  lesser  from  the  greater,  the  result  being  the  Long,  in  time 
which  turn  into  degrees,  etc.,  thus:  — 
h.          m.          s. 
Long.  4          41  2 

15 
60 
10  15  30 


70          15        30 

Named  E.  or  W.  thus:    Gr.  M.  T.  best,  Long.  W. 
G.  M.  T.  least,  Long.  E. 

Analysis 

4  x  15  =  60° 

41  -f  4  =  10   with  1  rem. 
m. 

1  x  15  =  15' 
Sec. 

2  x  15  = 30" 

70°        15'         30" 

On  the  principle  that  in  1  hour  of  time  are  15°  of  Long. ; 
in  4  min.  of  time,  1°  of  Long. ;  and  in  4  sec.  of  time,  1'  of 
Long. 

This  reduction  can  also  be  made  from  Table  7  Bowditch ; 
abreast  4-40  is  70°  then  abreast  of  1  m.  is  15',  and  abreast 
of  2  s.  is  30" ;  but  it  will  be  found  in  practice  that  the  com- 
putation can  be  made  while  one  is  hunting  up  the  table. 
Long,  being  found  at  time  of  sight,  carry  it  forward  to  Noon 
by  using  the  probable  forenoon  run  in  Mid.  Lat.  Sailing  by 
Inspection  as  follows:  Enter  Table  II  with  the  T.  C.  and 
Dist.,  opposite  in  D.  L.  col.  will  be  D.  L.  to  be  applied  to 
Lat.  used  at  sight  and  deduce  Mid.  Lat. ;  also  the  Dep. ; 
with  Mid.  Lat.  as  a  Course,  enter  Table  II  and  find  the  Dep. 
in  D.  L.,  col.,  opposite  in  the  Dist.  Col.  will  be  found  D.  Lo. 
Apply  this  to  Long,  at  sight,  and  if  the  Lat.  by  Obs.  at  Noon 
agrees  with  the  one  used  in  the  sight  and  afterwards  carried 
forward,  this  Long,  may  be  assumed  to  be  correct.  If,  how- 
ever, the  Lat.  is  found  to  be  in  error,  a  cor.  is  to  be  taken  from 
Table  38  Bowditch,  which  cor.  for  1  mile  of  Lat.  is  to  be 

(26) 


picked  out  and  noted  in  the  morning  when  the  sight  is 
worked.  An  examination  of  this  table  shows  that  the  ap- 
proximate Lat.  is  found  at  the  top,  sun's  alt.  and  polar 
dist.  at  side  and  the  cor.  at  the  junction  is  the  error  in  Long, 
due  to  1'  error  in  Lat. ;  then  if  at  Noon  the  Lat.  is  found  to 
be  3'  in  error  Cor.  x  3  =  cor.  to  be  applied  to  the  Long,  in 
A.  M.  further  North  further  East;  further  South,  further 
"West;  P.  M.,  the  opposite.  If  this  is  forgotten,  it  can  be 

seen  on  the  Sumner  Line 

A.  M. 


that  the  further  North  the  Lat.  is,  the  Long,  goes  to  the  East- 
ward. This  work  being  all  done  in  the  morning  and  the  Lat. 
Constant  established  (see  Work  Form,  Chap.  II,  Art.  1) 
nothing  remains  at  Noon  but  to  apply  Obs.  Alt.  to  the  con- 
stant as  already  explained  in  said  Art.  and  the  cor.  to  the 
Long,  for  error  in  Lat.  if  any,  and  in  a  moment  after  eight 
bells,  the  navigator  can  hand  the  captain  his  .position. 


See  note  in  front  of  book,  explaining  use  of  Table  46 
(1914  edition  of  Bowditch),  also  finding  declination  and 
equation  of  time  corrected  for  every  two  hours  in  editions  of 
American  Nautical  Almanac  since  1915. 


(27) 


Article  3  (a). 


Long. 


Sumner. 
Work  Form. 


w. 
c.-w. 

Ap.Dec. 

Cor. 

H.D. 
Hrs. 

Chro. 
Error 

Cor.  Dec. 
90 

G.M.T. 
12 

P- 
Ap.Eq.T. 
Cor. 

H.D. 
Hrs. 

G.M.A.T. 
24 

Cor.Eq.T 

h. 
L. 
P- 

Sec. 
Cosec. 

Cos. 
Sin. 

Int.                     =  hrs. 
h. 
L.                        Sec. 
p.                        Cosec. 

2) 

2) 

is.                       Cos. 
h. 

is 
h. 

is-h.                    Sin. 

is-h. 

L.Ap.T. 
Eq.T. 

2) 

2) 

L.AP.T.          sin. 

Eq.T. 

Sin. 

L.M.T. 
12 

L.M.T. 
12 

L.M.A.T. 
G.M.A.T. 

L.M.A.T. 
G.M.A.T. 

15 

15 

D.L.  D.  Lo. 

Sumner  Line. 


Long. 


Dep. 


In  any  time  sight  it  is  just  as  well  to  apply  the  Eq.  T. 
to  G.  M.  T.  which  will  give  G.  A.  P.  T.  then  the  L.  Ap.  T.  will 
be  applied  to  G.  Ap.  T. 


(28) 


The  computation  is  the  same  as  for  an  ordinary  time 
sight,  only  more  of  it.  Assume  a  Lat.  10'  or  20'  each  side  of 
the  D.  R.  Lat.  and  work  with  each,  carrying  them  along  to- 
gether. Two  positions  will  be  the  result  which  laid  down  on 
the  chart  will  give  the  line  of  position  and  the  point  on  that 
line  of  the  nearest  known  Lat.  will  be  the  position  of  the 
ship.  Or  this  line  may  be  established  by  inspection  of 
Table  II,  using  a  formula  in  Mid.  Lat.  Sailing.  Enter  Table 
II  with  Mid.  Lat.  as  a  course,  find  D.  Lo.  in  Dist.  Col.,  op- 
posite in  col.  of  D.  L.  will  be  found  the  Dep. ;  look  for  D.  L. 
and  Dep.  to  most  nearly  correspond  and  the  degrees  at  top 
or  bottom  of  page  will  be  the  direction  of  the  Summer  Line ; 
and  since  this  line  is  always  at  right  angles  with  the  Az- 
imuth of  the  body,  if  the  sights  are  taken  when  as  near  the 
prime  vertical  as  possible,  the  line  would  run  nearly  N.  and 
S.  and  it  is  readily  seen  that  quite  a  large  error  in  Lat.  would 
not  affect  the  Long.  In  practice  it  is  found  that  an  error  of 
30'  of  Lat.  would  not  make  more  than  15"  in  Long. 

(b)  As  one  line  does  not  establish  a  position,  except 
that  it  is  known  to  be  somewhere  in  that  line  and  is  fixed 
by  the  nearest  known  Lat.,  it  is  desirable  to  have  two  lines 
as  near  at  right  angles  as  possible,  then  the  point  of  inter- 
section is  the  position.    When  two  stars  are  available  whose 
Azimuths  differ  about  90°,  the  resulting  lines  of  position  are 
excellent.    If  the  sun  is  used,  the  two  lines  may  be  found 
by  taking  a  sight  in  the  morning  and  again  in  the  afternoon, 
carry  the  A.  M.  line  forward  by  D.  R.  to  the  time  of  the 
P.  M.  sight  and  plot  the  two  on  the  chart. 

(c)  As  has  been  stated,  the  line  of  position  is  always  at 
right  angles  to  the  Azimuth  of  the  body,  consequently  by  find- 
ing the  true  Azimuth,  the  line  of  position  may  be  at  once 
laid  down  at  right  angles  to  it  and  without  working  the  sight. 
This  method  is  a  little  too  lazy,  however,  to  be  conducive  to 
accuracy. 


(29) 


Article  4.  By  a  Fixed  Star. 

Work  Form. 


Chro. 
Slow 

R.A.  * 
Dec.   * 

P- 

90 

G.M.T. 
12 

Dip.- 
Ref.- 

G.M.A.T. 
R.A.M.S. 

Red.Table  9 

Obs.Alt. 
Cor. 

G.  S.  T. 

h. 
Lat. 
P- 

Sec. 
Cosec. 

s.  Cos. 

h. 


s-h  Sin 

H.A.±  E.  orW.  Sin. 

R.A.  * 

L.S.T. 

G.  S.  T.   ______ 

Long,  in  time 

15 


Long.  E.  orW. 


To  the  Chro.  time  apply  the  error,  finding  G.  M.  T.  and 
if  A.  M.,  turn  into  Astronomical  Time  by  adding  12  to  the 
hours. 

From  Page  II  of  the  almanac,  find  the  sun's  Right  As- 
cension for  the  date,  and  from  Table  9,  the  reduction,  which 
is  additive  to  mean  time.  Add  together  these  three  items  and 
the  result  is  G.  S.  T. 


(30) 


Take  the  R.  A.  from  the  almanac,  table  of  star  places, 
also  pick  out  the  Dec.  and  apply  it  to  90°  by  this  rule  to  find 
the  Polar  Dist.  (P.)  If  Lat.  and  Dec.  are  of  different  names, 
add;  same  names,  subtract.  Correct  star's  alt.  for  Dip.  and 
Eel ;  result  marked  h.  Add  together  h.,  Lat.  and  p.  and  from 
the  half  sum  subtract  h.  In  table  44,  find  sec.  of  Lat.,  cosec, 
of  p.,  cosine  of  the  half  sum  and  sine  of  the  remainder.  Half 
the  sum  of  these  four  logs  will  be  sine  of  the  H.  A.,  named  E. 
or  W.  as  the  sight  is  A.  M.  or  P.  M.  Convert  this  H.  A.  into 
sidereal  time  as  follows :  —  Sidereal  time  is  equal  to  the 
sum  of  the  right  ascension  of  the  body  and  its  H.  A.  subtract- 
ing 24  h.  when  the  sum  exceeds  that  amount.  If  the  H.  A. 
is  E.,  find  it  W.  by  subtracting  it  from  24  h.  and  then  add 
the  R.  A.,  or  a  shorter  way  is  to  mark  the  Easterly  H.  A. 
minus  and  the  R.  A.  plus,  and  subtract;  the  result  will  be 
the  same.  Having  found  the  local  sidereal  time  (L.  S.  T.), 
bring  down  G.  S.  T.  and  subtract  the  lesser  from  greater, 
leaving  the  Long,  in  time  which  turn  into  degrees,  minutes 
and  seconds  as  explained  in  Art.  I  of  this  chapter.  The 
Long,  is  named  E.  or  W.  by  this  rule :  — 
G.  S.  T.  least,  Long.  E. 
'  G.  S.  T.  best,  Long.  W. 

Note.  —  The  H.  A.  of  a  star  or  planet  is  always  taken 
from  the  P.  M.  column.  The  work  in  this  Art.  is  also  good  for 
a  planet,  but  it  is  not  as  good  to  use  as  the  corrections  vary, 
and  the  Dec.  &  R.  A.  must  be  very  carefully  corrected.  A 
planet  is  next  to  the  moon  in  the  amount  of  change  in  the 
data. 


(31) 


CHAPTER    IV. 


Compass  Error  and  Deviation. 

Article  1.  Azimuth. 

Work  Form. 

H.D. 

Chro.  Ap.  Dec.  Hrs. 

Error  Cor.  Cor. 

G.M.T.~~  Cor.DecT" 

12  90 


G.M.A.T.  p. 

24  Dip.-  S.D.+ 

Int.  from  noon  F=  hrs.         Ref .-  Par.  + 

_  i 

Obs.  Alt.  Cor.+ 

Cor.  +     

h.  Sec. 

Lat.  Sec. 

P- 

2) 


s.  Cos. 

P- 

s-p.  Cos. 

2  I 

i  T.  Az.  Cos. 


T.  Az. 
Comp,  Az. 
Comp.  Error 

Var.          

Dev. 


(32) 


The  azimuth  may  be  taken  at  any  time  but  the  most  fav- 
orable is  when  the  altitude  is  low.  It  is  often  taken  at  the 
meridian  passage  using  the  apparent  time  of  passage  when 
the  sun  bears  South  (or  North)  but  this  bearing  is  apt  to 
be  unreliable.  It  is  always  a  good  plan  to  take  a  bearing  at 
the  time  of  taking  a  Long,  sight,  and  can  then  be  worked 
in  unison,  thereby  saving  some  labor.  If  the  problem  is  to 
be  worked  out,  add  together  the  corrected  alt.  Lat.  and  p., 
take  the  half  sum  and  subtract  p.  If  p.  is  greater  than  the 
half  sum  (s)  the  term  s-p.  will  have  a  negative  value  but 
this  does  not  affect  the  result.  From  Table  44  take  the  sec. 
of  the  Alt.,  sec.  of  the  Lat.,  cos.  of  the  half  sum,  and  cos.  of 
the  rem.  Half  the.  sum  of  these  four  logs  will  be  the  cos. 
of  half  the  true  azimuth,  reckoned  from  the  N.  in  North  Lat. 

and  from  the  S.  in  South  Lat.     In  North  Lat.  if  the  time  is 

* 

A.  M.,  read  the  azimuth  from  North  to  East ;  if  P.  M.,  read 
it  from  North  to  West.  Compare  the  True  Az.  with  the 
Comp.  bearing,  subtracting  the  lesser  from  the  greater,  and 
the  result  is  the  compass  error  which  is  named  E.  or  W.,  ac- 
cording as  the  True  Az.  is  to  the  right  or  left  of  the  compass 
Az.  Example : 


T.  Az. 
Comp.  Az. 
Error 


N. 

N. 


120 
125 


E. 
E. 


W. 


(33) 


In  making  use  of  the  above  rule,  imagine  yourself  stand- 
ing in  the  center  of  the  compass  facing  the  rim,  and  looking 
in  the  direction  of  the  bearings,  it  is  obvious  that  the  T.  Az. 
falls  to  the  left  of  the  Comp.  Az.  therefore  the  error  is  W. 
To  find  the  Dev.,  take  the  var.  from  the  chart,  a  pilot 
chart  is  the  best,  and  apply  it  to  the  error  with  its  opposite 
name;  like  names  add,  unlike  names  subtract,  and  give  to 
the  result  the  name  of  the  greater.  Example,  suppose  in  the 
last  case  the  var.  was  found  from  the  chart  to  be  4°  w. 

Error,  5°         W. 

Var.  _4 K 

Dev.  1  W. 

Now  suppose  the  navigator  is  not 'going  to  work  the 
problem,  which  as  a  matter  of  fact  he  never  does  if  he  has  a 
good  set  of  tables ;  we  will  return  to  the  beginning  and  start 
differently.  The  most  practical  tables  for  the  merchant  ship 
navigator  are  Burdwood  and  its  supplementary  Davis ;  these 
tables  are  figured  to  every  four  min.  of  time.  Work  up  your 
position  by  D.  R.  if  you  are  not  taking  any  other  obs.,  and 
find  the  error  of  your  watch  on  L.  Ap.  T.,  correct  the  de- 
clination ;  keep  ship  steady  on  her  course  and  note  the 
bearing  of  the  sun,  with  shadow  pin  or  azimuth  mirror,  at 
the  same  instant  note  the  time.  Apply  the  error  of  watch 
on  L.  Ap.  T.  and  enter  the  azimuth  table  with  the  Ap.  T. 
at  side  of  page  and  Lat.  and  Dec.  at  top,  taking  care  to  see 
whether  Lat.  and  Dec.  are  of  the  same  or  different  names; 
at  the  junction  of  these  columns  will  be  found  the  True  Az. 
If  the  Ap.  T.  doesn't  jibe  with  the  four  min.  intervals,  the 
tabulated  Az.  must  be  corrected  for  the  dif.  between  the  two. 
Many  times  the  navigator  can  help  himself  along  by  plan- 
ning ahead  a  little,  by  looking  at  the  table  before  taking  the 
bearing  and  see  where  the  Ap.  T.  falls,  then  note  on  a 
piece  of  paper  the  time  the  watch  will  show  and  wait  for  that 
min.  before  taking  the  bearing.  If  desirous  of  swinging  ship 
on  courses  about  to  be  steered  during  the  night,  and  three 
or  four  dev.  will  be  required,  prepare  a  table  ahead  thus : 

L.Ap.T.      Watch     P.  H.  Comp.     Stand     Comp.  Az. 
8.28 

.32 

.36 

.40 

(34) 


Knowing  how  much  the  watch  is  fast  or  slow  of  Ap.  T., 
it  is  easy  to  do  the  rest.  It  is  often  necessary  to  interpolate 
for  Lat.  if  the  Lat.  falls  half  way  between  two  degrees  and 
the  same  for  Dec.,  but  practice  will  show  the  navigator  how 
he  can  most  easily  do  this ;  for  instance,  if  a  Dec.  of  18°  gave 
79°  22'  and  19°  gave  78°  20',  the  dif.  for  1°  of  Dec.  is  1°  2' 
=  62' ;  suppose  the  Dec.  was  about  18°  20',  the  20'  is  y3  of 
a  degree,  and  %  of  62'  is  21'  nearly,  so  it  would  be  seen  at 
a  glance  that  21'  would  have  to  be  subtracted  from  79°  22' 
as  the  azimuth  is  decreasing  from  18°  to  19°  of  Dec.  The 
same  operation  to  interpolate  for  Lat.  It  may  look  to  the 
beginner  like  quite  a  complication  but  it  is  really  very  easy 
after  a  little  practice,  and  aboard  a  well  regulated  ship  there 
is  practice  enough  to  be  had  in  compass  work. 


Article  2.  Amplitude. 

Work  Form. 

Lat.  Sec. 

Dec,  Sin^ 

T.  Amp.  Sin. 
Comp.  Amp. 
Comp.  Error 


There  is  little  to  be  said  about  the  work  except  to  find 
the  sec.  of  the  Lat.,  the  sine  of  the  Dec.  and  add  them  to- 
gether ;  result  is  the  sine  of  the  true  amplitude  reckoned  from 
the  E.  or  W.  point.  The  compass  error  is  then  determined 
in  the  same  manner  as  already  described  in  the  Azimuth 
problem.  The  observation  is  best  taken  when  the  sun  is 
about  one  diameter  above  the  visible  horizon.  If  Burdwood's 
tables  are  used,  the  True  Amp.  is  given  for  the  Lat.  and  Dec. ; 
also  the  apparent  time  of  its  rising  and  setting. 

(35) 


CHAPTER     FIVE. 


As  a  practical  illustration  of  the  manner  in  which  the 
foregoing  problems  may  be  used  in  a  day's  navigational 
work  aboard  an  ocean  steamer,  let  a  case  be  assumed  in  which 
a  ship  capable  of  steaming  23  knots,  leaves  her  dock  in  New 
York  at  10  a.  m.  (Eastern  Standard  time),  March  18,  1914, 
and  having  discharged  her  Pilot,  arrives  at  Ambrose  Chan- 
nel Lightship  in  Lat.  40°  28'  N.  Long.  73°  50'  W.  at  11.50 
A.  M.,  and  her  clock  is  set  on  Local  Apparent  Time  (L.  Ap. 
T.),  which  is  found  as  follows:  — 


(75th  Meridian) 


h. 

m. 

s. 

E.  Stand.  Time 

11 

50 

00 

+  5 

G.  M,  T. 

16 

50 

00 

Long,  in  Time 

4 

55 

20 

L.  M.  T. 

11 

54 

40 

Eq.  T. 

-8 

22 

L.  Ap.  T. 

11 

46 

18 

Therefore  the  clock  is  retarded  3m.,  42s. 

Ship's  chronometer  showed  4h.  55m.  20s.  which  was 
fast  of  G.  M.  T.  5  m.  20  s.  and  gaining  1.5  s.  daily.  Set  course 
S.  76°  E.  for  first  turn  on  trans-Atlantic  track,  taken  from 
Pilot  Chart  of  May,  1912,  in  Lat.  40°  00'  N.  Long.  70°  00'  W. 

(36) 


The  formula  to  be  used  for  this  is  found  in  Chapter  I,  Art. 

1,  Case  1  —  Middle  Lat.  Sailing. 

Lat.  left         40°     28'  N.  Long,  left 


"  of  turn 
D.  L. 

Mid.  Lat. 
D.  Lo. 
Mid.  Lat. 
Dep. 
D.  L. 
T.  C.  S. 
Dist. 


40      00   N. 

28 


u  of  turn 
D.  Lo. 


73° 
70 


50' 
oo 


w. 
w. 


3      50 =230  miles 


14 


40 


80' 


14 

230  =  2.36173 

40     14  =  9.88276 

175.6  =  2.24449 

28  = 

56' E,  = 

177.7     = 


2.24449 

1.44716 

10.79733 


1.44716 

.80249 

2.24965 


Mean  variation  from  pilot  chart  10°  W.  Dev.  from 
compass  book  for  last  voyage,  5°  E.  Error  5°  W.  Course 
by  compass  S.  76°  E. 

At  3  P.  M.,  having  run  74  miles,  position  by  D.  E.  was 
found  by  inspection :  — 

Lat.  left    40°    28'  N.  Long,  left    73°    50'  W. 

D.  L.  12  S.  D.  Lo.         _l 35^  E. 

Lat.  in     ~40 16  N.  Long,  in     "72      15  W.  =4  h.  29  m 

Obs.  a  bearing  of  the  sun  with  azimuth  mirror,  finding 
it  to  be  S.  62°  51'  W.  Chro.  8h.  9m.  2s.  chro.  fast  5m.  20s. 

BURDWOOD'S  TABLES 
T.  Az.       N.  120°   9'W. 
Comp.Az.N.  117     9  W. 
Comp.Error      5     0  W. 
Var.  10     0  E.  (opp.name) 


Chro. 
Fast 


8 


9       2 
-5     20 


3 
49 


42 


G.M.  T.  8 

Long.     -4 

L.  M.  T.  3     14    42 

Eq.  T.  -8     17  (Cor.)  Dev' 

L.Ap.T.    3     6     25 


5     0  E. 


(True  to  the  left,  error  is  W.) 

(37) 


At    5    P.    M.,   having    sailed   120    miles   on    the   T.   C. 
S.  81°  E.,  D.  R.  position  was  figured  by  inspection. 

Lat.  left    40°     28'    00  N.  Long,  left     73°     50'  W. 

D.  L.  18     48  S.  D.  Lo.  2      35   E. 

Lat.  in 


40 


9      12  N. 


Long,  in        71       15  W- 


Obs.  Alt.  O   8°  44'.    Height  of  eye  35  feet.    Chro.  lOh. 
9m.  2s.  fast  5m~20s.    Bearing  by  compass  S.  86°  40'  W. 


Chro. 
Error 


h  m  s 
10  9     2 
-5  20 


G.M.T.  10  3  42  =  10.06 


Ap.Dec.  1°  10'  20.8"  S. 
Cor.              -9  56.5 

H.D.  59.29" 
*10.06 

Cor.Dec.  1     0  24.3  S. 
90 

35574 
5929 

p.     91     0  24 


596.4574 


Dip.  -5' 

48" 
2 

S.  D.  +16' 
Par.      + 

6" 
9 

s. 
22.68 
7.35 

s. 
H.D.   .731 
*10.06 

-11 

50 

+16 
-11 

15                    m. 
50         Eq.T.  8 

+4 

25         Cor. 

Cor.Eq.T+8 

15.33 

4386 
731 

7.35386 


*See  note  in  front  of  book  relative  to  declination  and 
equation  of  time  being  corrected  for  every  two  hours  in 
American  Nautical  Almanac. 


(38) 


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(39) 


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At  10  P.  M.     D.  R.  position  of  next  noon  was  worked. 
T.  C.     S.  84°  E.    Dist,  360  miles. 

Lat.  7.35     40°       00'  N.  Long.  7.35  P.M.   70°       00' W. 

D.  L.          37  S.  D.  Lo.  _1_ 45  E. 

Noon  Lat.  ~39         23  N.  Long.  Noon  62~~     15  W. 

MI>.  L.     18  4h.    9  m 

Mid.  Lat.    39        41 

h     m     s  D.  Lo.  465  miles 
Ship's  clock     10   00   00 

h  m     s 

Chro.  392 

Fast  -5    21 
G.M.T.         15      3    41  (Add  12  hours) 

Eq.  T.  -8      2  (Cor,  for  Gr.  time 

G.Ap.T.     14  55    39  next  noon) 

Noon  Long.    4     9    00 

L.  Ap.  T.      10  46    39  (For  noon) 

From  this  work,  the  clock  is  found  to  be  46  m.  39  s.  slow. 
11  P.  M.,  advanced  clock  46  m.  39  s.  to  L.  Ap.  T.  for  next 
noon,  and  sent  a  slip  to  the  Chief  Engineer  and  Chief  Stew- 
ard. 

Mar.  19th,  5  A.  M.,  D.  R.  position  was  worked,  not  for- 
getting the  allowance  of  46  m.  39  s.  advance  in  the  clock. 
T.  C.  S.  84°  E.  Dist.  197  miles. 

Lat.  7.35  P.M.   40°   00'  N.         Long.  7.35  P.M.    75°   00'  W 

D.  L.  21^8.          D.  Lo.  _4 15  E. 

Lat.  5.00  A.M.  39     39~N.          Long.  5.00  A.M.    65     45  W. 
Dep.  195.9  D.  Lo.  255  4h.  23m. 


(42) 


Obs.  Alt.  *  Polaris     38°  59'  Chro.     9h.     22m.     23s. 

Chro.  fast    5  m.     21  s.  Height  of  Eye,  35  ft. 

h     m      s  h     m      s 

Chro.  9     22     23  L.M.A.T.  16     54      2 

Fast  -5     21  Red.  Tab.  Ill  2    47 

G.  M.  T.         9     17      2  G.  S.  T.  23    40    48 

12 Red.  for  Long      +43 

G.M.A.T.  21  17   2  40  38  20 

Long.      4  23  24 

L.M.A.T.  16~~54 2        L.  Sid.  T.    16  38  20 
(Mar.  18)  25  28  36 

H.  A.  *      8  50  16 
Dip.  -5'  48" 

Ref.  -1 12^ 

Cor.  -7  00        Obs.  Alt.  *    38°  59' 

Cor.         -7_ 

True  Alt.  38       52 

Cor.  Tab.  I  +47 

Lat.  5.00A.M.  39      39  N. 

At  the  instant  of  taking  the  Alt.  of  Polaris,  another  of- 
ficer observed  the  Alt.  of  *  Altair  in  the  East,  finding  it  to 
be  38°  4'  45".  Chro.  9h.  22m.  23s.  Chro.  fast  5m.  21s. 
Height  of  eye,  35  feet. 


(43) 


h  m  s 
19  46  35 

8  38  25  N. 
90  _ 
81  21  35 
G.M.A.T.  21  17   2 


h     m     s 

Chro. 

9    22    23 

R.  A.  * 

Fast 

-5    21 

Dec. 

G.M.T. 

9    17      2 

12 

P- 

R.A.M.S.  23  40  48         i'  88°  4  45   ^  ~5  48' 
Red.(Tab.9)  3  30 
—  ~ 


45    20    h'     37  5T  45   Cor'  ~6  59 
24          L.     39  39  00  sec.    .11353 

'      81  21  35  cosec.  .00496 


Gr  S  T   21   120 


2  )158  58  20 

s.      79  29  10  cos.   9.26120 
h.     37  57  45 


H. 
R. 
L. 
G. 

A. 
A. 

S. 
S. 

* 

T. 
T. 

s-h. 

-3 
+19 

41  31  25  sin.   9, 

,82147 

7  57  E. 
46  35 

2)19, 

20116 

sin.   9 

,60058 

16 
21 

38 
1 

38 
20 

Long,  in  time  4  22  42 

15 

60 
5  30 

10  30 
65  40  30  W. 


As  a  result  of  these  two  observations  at  the  same  mo- 
ment, the  exact  position  is  obtained  without  an  element  of 
D.  R.  entering  in.  At  sunrise  occurring  at  6  h.  3  m.  L.  Ap.  T., 
an  amplitude  should  be  observed;  preparing  for  this,  the 
Officer  of  the  Deck  finds  his  approximate  position  at  that 
time  will  be  Lat.  39°  36'  N.  Long.  65°  6'  W.  Var.  15°  W. 
Dev.  (probably)  6  E.  T.  C.  S.  84°  E.  Dist.,  30  miles. 


(44) 


Lat.  5 

A.M. 

39° 

39'  N. 

Long. 

5A.M.    65° 

40' 

w. 

D.  L. 

3   S. 

I). 

Lo. 

39 

E. 

Lat. 

39 

36  N. 

Long. 

65 

1 

W. 

Dep. 

29 

.8 

D.Lo. 

39 

4h.  20 

m. 

4s. 

h. 

m 

s. 

L.  Ap. 

T 

.  Sunrise 

6 

3 

Long. 

4 

20 

4 

G.  Ap. 

T 

. 

10 

23 

4 

D.  R., 

Noon 

Long. 

4 

9 

0 

Ship's 

Clock 

6 

14 

4 

Therefore  at  6h.  14m.  ship's  time,  the  bearing  of  the 
rising  sun  when  one  diameter  above  the  horizon  was  taken 
and  found  to  be  E.  10°  30'  S. 

BURDWOOD'S  TABLES. 


(Opposite  name) 


BY  COMPUTATION. 

Lat.  39°         36'  Sec.     .11322 

Dec.  0          48  Sin.  8.14495 


T.  Amp. 
Comp.  Amp. 
Error 
Var. 
Dev. 

E. 
E. 

1° 
10 

18' 
30 

S. 
S. 

9 
15 

12 

W. 
E. 

5 

48 

E. 

T.Amp.  E.     1  Sin.   8.25817 

Knowing  the  exact  Dev.,  the  obs.  position  at  5  A.  M.  is 
carried  forward  to  8  A.  M.  Var.  14°  50'  W.  T.  C.  S.  84°  E. 
Dist.,  69  miles. 


Lat.5 
D.  L. 

Lat.  ! 

A.M.     39° 

39'  N. 

7    S. 

Long. 
D.  Lo 
Long. 

5A.M. 

8A.M. 
D.  Lo. 

65°     40'  W. 
1       29     E. 

3  A.M.       39 
Dep. 

32  N. 
68.6 

64      11    W. 

89 

The  Officer  prepares  a  slip  containing  obs.  position  8 
A.  M.  and  compass  error  sending  it  to  the  Captain,  when  he 
turns  out. 

(45) 


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Lat.  Light-ship  40°  28'  N. 
Lat.  in      39  23  N. 
D.  L.        1   5  =  65' 
|D.  L          32 
Mid.  Lat.    39  55 


Long.  Light-ship  73°  50'  W. 
Long,  in       62  13  W. 
D.  Lo.         11  37  E. 
697' 


CASE  I.      MID.  Lat.  SAILING. 


D.  Lo. 
Mid.  Lat. 
Dep. 
D.  L. 
T.  C. 
List. 


2.84323 
9.88478 
2.72801 
1.81291 

S.  83°  4'  E  =  Tan.  10.91510 
538.5  =  Log. 


697   =  Log. 

39  55   =  Cos. 

534.6  =  Log. 

65   = 


1.81291 

.91824 

2.73115 


Noon  position.    Lat.  39°  23'  N.    Long.  62°  13'  W. 

T.  C.  made  good  S.  83°  4'  E.    Disk,  538.5  miles. 

D.  Lo.   11°  37'  =  46m.  28s. 

Length  of  day,  23  h.  13m.  32s.    Additional  time  from  the 

lightship  to  noon,  Mar.  18,  13  m.  42  s.     Total  time, 

23  h.  27m.  14s. 
Average  speed,  22.9  knots. 


(52) 


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(53) 


CHAPTER  SIX. 


Definitions  —  Navigational  Terms. 


Latitude  (Lat.)  —  The  distance  N.  or  S.  of  the  Equator. 
Longitude  (Long.)  — The  distance  East  or  West  of  a  given 

Meridian  called  the  Prime  Meridian.     The  meridian  of 

Greenwich  has  been  generally  adopted. 

Difference  of  Latitude  (D.  L.)  —  The  distance  in  a  N.  or  S. 
direction  between  any  two  points  on  the  Earth's  surface. 

Difference  of  Longitude  (D,  Lo.)  —  Is  the  arc  of  the  Equator 
intercepted  between  two  meridians;  measured  in  de- 
grees, minutes  and  seconds. 

Departure  (Dep.) — The  actual  distance  sailed  in  an  East  or 
West  direction.  Also  the  last  known  point  left  in  dead 
reckoning. 

Dead  Reckoning  (D.  R.)  —  Guess  work.  Keeping  the  run  of 
the  ship  by  her  courses  and  distances ;  always  of  doubt- 
ful accuracy,  yet  necessary. 

Day's  Work  —  The  problem  of  D.  R.  which  includes  the 
record  of  the  ship  's  run  for  24  hours,  the  Traverse  Table 
being  the  Compass  Courses,  Variation,  Deviation  and 
Leeway ;  True  Courses,  Distances  and  the  North,  South, 
East  and  West  columns  of  D.  L.  and  Dep.  From  this 
is  worked  the  ship 's  position  by  any  of  the  various  sail- 
ings. 

Variation  (Var.)  —  That  part  of  the  Compass  Error  due  to 
the  difference  in  positions  of  the  geographical  and  mag- 
netic poles  of  the  earth.  The  amount  of  the  Var.  de- 
pends on  the  angle  between  these  two  poles  at  the  po- 
sition of  the  observer  which  changes  with  the  locality 
and  the  year. 

(54) 


Deviation  (Dev.)  — That  part  of  the  Compass  Error  due  to 
masses  of  magnetic  metal  within  the  ship  itself. 

Local  Attraction  —  That  part  of  the  Compass  Error  due  to 
natural  magnetic  attraction  in  the  vicinity  of  the  vessel. 

Compass  Error  —  The  difference  between  the  compass  and 
the  true  direction ;  or  its  total  error. 

True  Course  —  Is  the  compass  course  corrected  for  all  er- 
rors ;  Westerly  Error  to  the  left ;  Easterly  to  the  right. 

Magnetic  Course  —  Is  the  compass  course  with  all  errors 
applied  except  the  Variation;  courses  taken  from  the 
chart  are  Magnetic  if  the  inner  compass  is  used. 

Zenith  —  Is  the  point  in  the  heavens  directly  over  the  ob- 
server's head. 

Celestial  Equator  or  Equinoctial  —  Is  the  great  circle  formed 
by  extending  the  plane  of  the  Equator  until  it  intersects 
the  celestial  sphere. 

Declination  —  Is  the  distance  of  a  heavenly  body  from  the 
Equinoctial  either  N.  or  S.  N.  declinations  may  be 
regarded  as  positive  (+)  and  S.  declination  as  neg- 
ative ( — ). 

Polar  Distance  (P.  D.)  —  Is  the  distance  of  a  heavenly  body 
from  the  pole  nearest  the  observer. 

Altitude  (Alt.)  — Is  the  distance  of  a  heavenly  body  above 
the  horizon. 

Zenith  Distance  (Z.  D.)  —  Is  the  distance  of  a  heavenly  body 
from  the  zenith. 

Hour  Angle  — Is  the  angle  at  the  pole  between  the  meridian 
of  the  observer  and  the  hour  circle  passing  through  the 
body. 

Hour  Circles  —  Are  formed  by  extending  the  planes  of  the 
terrestrial  meridians  until  they  intersect  the  celestial 
sphere. 

(55) 


Azimuth  —  Is  the  bearing  of  a  heavenly  body  measured  from 
N.  or  S.  towards  E.  or  W.  according  as  the  Lat.  is  N.  or 
S.  and  the  position  of  the  body  E.  or  W.  of  the  me- 
ridian. 

Amplitude  —  Is  the  bearing  of  a  body  in  the  horizon. 

Ecliptic  —  Is  the  path  the  sun  appears  to  move  in  by  reason 
of  the  annual  revolution  of  the  earth. 

Equinoxes —  Are  those  points  on  the  Celestial  Equator  where 
the  sun  seems  to  cross  it  in  changing  declination.  The 
point  of  crossing  from  Southern  to  Northern  declination 
is  the  Vernal  Equinox,  also  designated  as  the  First 
Point  of  Aries  and  is  used  as  an  origin  for  reckoning 
right  ascension. 

Right  Ascension  —  Is  the  celestial  longitude  of  a  heavenly 
body  measured  from  the  First  Point  of  Aries  Eastward 
through  24  hours. 

Great  Circles  —  Divide  the  Earth  into  two  equal  parts. 
Small  Circles  —  Divide  the  Earth  into  two  unequal  parts. 

Meridians  —  Are  great  circles  passing  through  the  poles,  and 
are  used  in  measuring  Long. 

Parallels  —  Are  small  circles  extending  around  the  Earth 
parallel  to  the  Equator,  and  are  used  for  measuring  Lat. 

Equator  —  Is  a  Great  Circle  extending  around  the  Earth 
midway  between  the  poles,  at  right  angles  to  the  me- 
ridians. 

Prime  Meridian  —  Any  meridian  agreed  upon  as  a  unit  from 
which  to  reckon  Long. 

Observed  Altitude  (h.) — The  altitude  of  a  heavenly  body 
as  read  from  a  sextant. 

Index  Correction  —  An  error  of  the  sextant  that  ought  not 
to  be  allowed  to  remain;  but  if  it  appears  it  must  be 
applied  to  h. 

Dip  —  A  correction  to  be  subtracted  from  h.  owing  to  the 
height  of  the  eye  above  sea  level. 

(56) 


Refraction  (Ref.) — A  correction  to  be  subtracted  from  h. 
owing  to  the  rays  of  the  sun  being  deflected  by  the  at- 
mosphere. 

Parallax  (Par.)  — A  correction  to  be  added  to  h.  changing 
it  from  the  surface  of  the  Earth  to  its  center. 

Semi-Diameter  (S.  D.) — A  correction  to  be  applied  to  h. 
if  it  is  of  the  sun  or  moon.  Additive  if  the  lower  limb  is 
observed ;  subtractive  if  the  upper.  It  corrects  h.  to  the 
center  of  the  body. 

Apparent  Time  or  Solar  Time  —  Is  the  hour  angle  of  the  cen- 
ter of  the  sun.  Owing  to  lack  of  uniformity  of  the  sun's 
motion  this  time  cannot  be  used  as  a  standard. 

Mean  Time  —  Is  the  hour  angle  of  the  mean  sun,  a  fictitious 
body  invented  for  the  purpose  of  overcoming  the  irreg- 
ularities of  the  real  sun;  and  given  a  uniform  motion. 
The  two  suns  coincide  at  the  First  Point  of  Aries. 

Equation  of  Time — The  difference  between  apparent  and 
mean  time. 

Sidereal  Time  —  Is  the  hour  angle  of  the  First  Point  of  Aries. 

Astronomical  Time  —  Commences  at  noon  of  the  civil  day  of 
the  same  date,  is  reckoned  from  0  h.  to  24  h.  The  civil 
day  begins  12  hours  before  the  astronomical  day.  • 


(57) 


CHAPTER  SEVEN. 


CHARTS. 

Navigation  by  this  means  is  very  simple  as  well  as  very 
useful,  and  a  careful  examination  of  the  chart  of  a  locality 
will  frequently  uncover  to  the  observer  facts  hitherto  un- 
known to  him.  In  using  the  U.  S.  Government  charts,  it  is 
well  to  remember  that  the  soundings  outside  the  dotted  sur- 
faces are  expressed  in  fathoms  and  are  referred  to  mean 
low  water,  while  a  shoal,  rock,  or  reef  will  be  shown  by  a 
dotted  surface  with  the  depth  of  water  in  feet.  Strong  tides 
are  indicated  by  little  arrows,  the  direction  of  the  arrows 
showing  the  set.  Where  heights  are  expressed,  such  as  on 
a  bold  mountainous  coast,  they  are  in  feet  from  mean  high 
water  mark.  Curves  are  generally  shown  on  general  charts 
at  50  and  100  fathoms  and  often  up  to  greater  depths,  en- 
abling a  navigator  to  follow  a  line  of  soundings  in  the  thick 
weather,  thus  checking  his  position.  To  find  a  course  and 
distance  by  chart,  indicate  by  a  pencil  dot  the  position  of 
the  vessel  and  another  at  the  point  aimed  at ;  place  the  par- 
allel rule  with  the  same  edge  cutting  both  points  and  walk 
it  to  the  nearest  compass  rose  and  the  point  of  the  compass 
touched  by  the  edge  of  the  rule,  when  it  cuts  the  center,  is 
the  course,  taking  care  to  read  it  from  the  inside  compass 
which  gives  the  magnetic  direction;  the  outside  ring  is  the 
true  direction  —  the  variation  changes  with  the  locality. 
With  the  dividers  spread  between  the  points  measure  on  the 
scale,  or  on  the  division  at  sides  of  chart,  not  at  top  or  bottom, 
to  find  the  distance  in  nautical  miles.  If  the  distance  is  large, 
spread  the  dividers  to  a  convenient  distance  and  step  off  be- 
tween the  points. 

(58) 


Rules  of  the  Road. 


AIDS     TO     MEMORY. 

BY  THOMAS  GRAY. 

When  both  side  lights  you  see  ahead, 
Port  your  helm  and  show  your  Eed, 
Green  to  Green,  or  Eed  to  Red, 
Perfect  safety  —  go  ahead ! 

If  to  your  starboard  Red  appear, 

It  is  your  duty  to  keep  clear ; 

To  act  as  judgment  says  is  proper :  — 

To  port,  or  starboard,  back,  or  stop  her ! 

But,  when  upon  your  port  is  seen 
A  steamer's  starboard  light  of  Green, 
There's  not  so  much  for  you  to  do, 
For  Green  to  port  keeps  clear  of  you. 

Both  in  safety  and  in  doubt, 
Always  keep  a  good  lookout. 
In  danger  with  no  room  to  turn, 
Ease  her !    Stop  her !    Go  astern. 

If  close  hauled  on  the  starboard  tack, 
No  other  ship  can  cross  your  track ; 
If  on  the  port  tack  you  appear, 
Ships  going  free  must  all  keep  clear ; 
While  you  must  yield,  when  going  free, 
To  sail  close  hauled,  or  on  your  lee. 
Both  free  with  wind  on  different  sides, 
Art.  17  C.  your  case  decides. 
And  if  you  have  the  wind  right  aft, 
Keep  clear  of  every  sailing  craft. 
(59) 


PRACTICAL       ILLUSTRATIONS 


Article  1. 


The  duty  of  each  is  plain,  blow  1  whistle,  port  the  helm 
and  swing  to  starboard,  passing  on  each  other's  port  hand. 
This  is  done  when  both  lights  are  seen  on  each  steamer  at 
night;  or  when  the  masts  of  each  are  seen  to  be  in  a  direct 
line  in  the  day  time.  Either  vessel  may  blow  the  whistle 
first. 

A 


If  however,  their  courses  are  so  far  to  starboard  of  each 
other,  but  on  parallel  lines,  as  to  render  passing  on  that  side 
safe,  each  continues  on  his  course,  and  if  whistles  are  ex- 
changed, the  two  blast  signal  is  used. 

Article  2. 


B.  has  A.  on  his  starboard  side,  therefore  A.  has  right 
of  way.  B.  blows  1  whistle  which  A.  answers  with  1 ;  B. 
then  ports  his  helm  and  stops  and  backs  if  necessary.  A. 
maintains  his  course  and  speed. 

(60) 


This  may  be  complicated  by  the  entrance  of  C. 

B 


A.  still  has  the  right  of  way  over  B.  but  C.  has  it  over  A. 
B.  may  blow  1  whistle  which  may  be  answered  by  both  A. 
and  C. ;  then  A.  blows  1  to  C.,  who  answers  it.  A.  ports  his 
helm  to  go  around  the  stern  of  C.  B.  ports  his  helm  in  order 
not  to  cramp  A.  C.  continues  on  but  may  port  a  little  or 
slow  down  or  both,  in  order  not  to  shave  B.  too  closely. 

It  may  be  complicated  still  further  by  D. 


This  looks  bad  but  -it  isn't,  provided  everybody  does 
the  shipshape  thing.  All  hands  may  blow  1  whistle  and  port ; 
but  lest  there  may  be  a  greenhorn  in  one  boat,  it  would 
be  the  best  judgment  for  them  to  stop  and  back  until  whistles 
are  exchanged  and  understood. 

(61) 


Article  3. 


A  B 

Here  A.  is  supposed  to  be  the  faster  of  the  two,  con- 
sequently blows  1  whistle  if  he  wishes  to  pass  on  B.  's  star- 
board side  or  two  whistles  on  the  port  side.  Whichever  sig- 
nal is  given,  is  answered  by  B.  and  A.  is  justified  in  passing. 
If  however,  B.  sees  some  reason  that  A.  doesn't  which  would 
render  such  passing  unsafe,  B.  gives  the  danger  signal  of 
several  short  blasts,  iiot  less  than  4,  whereupon  A.  must 
stop  and  keep  astern  of  B.  until  B.  is  ready  for  A.  to  pass ; 
when  B.  will  give  the  signal. 

B 


Still  assuming  A.  to  be  the  faster,  this  is  a  bad  situation. 
The  law  says  that  any  vessel  coming  up  on  another  vessel 
from  a  direction  more  than  two  points  abaft  her  beam  is  an 
overtaking  vessel ;  to  be  determined  in  the  night  by  a  sight 
of  her  side  lights ;  but  if  in  the  day  time  a  doubt  exists  as 
to  the  bearing^  she  must  consider  herself  an  overtaking  ves- 
sel and  act  accordingly.  It  sounds  good  in  theory  but  the 
trouble  is  nobody  ever  takes  a  bearing  to  determine  whether 
or  not  he  is  an  overtaking  vessel. 

In  the  diagram,  A.  is  without  doubt  an  overtaking  ves- 
sel, but  place  her  between  the  dotted  lines  and  as  far  from 
the  beam  bearing  as  possible  and  what  happens  ?  No  one  can 
tell  exactly  by  his  eye  just  which  side  of  the  line  he  is,  and  as 
stated  above,  a  bearing  is  rarely  taken.  In  the  diagram  A. 
says  he  is  forward  of  the  line  and  holds  his  course  and 
speed  because  in  a  crossing  situation  he  has  the  right  of  way ; 
B.  says  A.  is  certainly  an  overtaking  vessel  and  pays  no  par- 
ticular attention  to  him,  believing  A.  knows  his  business 
and  will  slow  down  and  cross  his  stern ;  neither  one  takes 

(62) 


a  bearing  and  presently  they  come  together  with  each  one 
claiming  that  he  observed  the  rules,  and  believing  it  too. 
Always  proceed  with  caution  in  this  situation,  and  if  in  any 
position  abaft  the  beam  of  the  other  vessel,  give  him  the 
benefit  of  the  doubt. 

A 


Here,  however,  it  doesn't  matter,  because  A  must  keep 
out  of  the  way  whether  it  be  an  overtaking  or  a  crossing  po- 
sition. 

If  A.  should  happen  to  be  a  sailing  vessel,  it  makes  no 
difference,  for  in  the  overtaking  situation,  if  a  sailing  vessel 
happens  to  be  faster  than  the  steamer,  it  is  well  to  remember 
that  Art.  24  applies  and  takes  precedence  over  Art.  20.  There 
are  men  sailing  boats  who  have  overlooked  Art.  24,  and  be- 
lieve that  there  is  no  situation  in  which  a  sailing  vessel  shall 
keep  out  of  the  way  of  a  steamer. 

Article  4. 
A 


C 


In  this  situation  it  looks  at  first  glance  as  though  A 
would  pass  B.  on  his  port  hand,  but  suppose  C.  hasn't  seen 
A.  and  follows  the  law  by  holding  to  that  side  of  the  channel 
on  his  own  starboard  hand,  gives  B.  1  whistle  and  ports  his 
helm?  A  mix-up  may  occur.  Therefore  the  best  thing  A. 
can  do  is  to  give  B.  1  whistle  and  if  answered  with  1  to  port 
his  helm,  passing  B.  on  his  starboard  hand ;  by  so  doing,  he 
gives  C.  the  opportunity  to  observe  the  law.  Better  still  for 
A.  to  stop  for  a  minute  until  he  sees  just  what  C.  is  going  to 
do. 

(63) 


Article  5. 


B 


Shoal. 


Shoal. 


It  is  plain  that  the  burden  of  this  situation  rests  upon  A. 
and  C.  B.  has  a  tow  and  a  fair  tide  and  can't  do  anything 
in  the  way  of  stopping.  A.  certainly  has  the  right  of  way 
over  C.,  but  as  C.  is  about  to  head  into  the  channel  A.  is 
coming  out  of,  when  the  two  vessels  will  come  about  head 
and  head,  it  is  proper  for  A.  to  at  once  blow  1  whistle  and 
port,  thereby  giving  C.  a  chance  to  round  the  buoy  without 
crowding  on  B. ;  A.  will  then  be  in  a  good  position  to  enter 
his  channel.  True  A.  might  say  "I  have  the  right  of  way 
and  shall  maintain  course  and  speed,"  this  would  be  in 
accord  with  Art.  21  of  the  Pilot  Rules ;  but  consider  the  spec- 
ial circumstances,  A.  is  nearly  out  of  a  narrow  channel  that  B. 
and  C.  are  about  to  enter;  B.  can't  stop  for  the  fair  tide 
will  sweep  his  barges  round  and  obstruct  the  channel;  C. 
could  stop,  but  in  the  position  they  are  about  to  get  into, 
A.  and  C.  will  be  in  the  head  and  head  situation  when  they 
are  supposed  to  blow  1  whistle  and  pass  on  the  port  side  of 
each  other,  according  to  Eule  I  of  the  Pilot  Rules;  quickly 
taking  all  these  things  into  consideration,  A.  remembers 
Art.  27  of  the  Pilot  Rules,  decides  not  to  be  a  "road  hog" 

(64) 


and  acts  as  above  stated.    Art.  27  is  here  given  in  full  with 
a  recommendation  for  its  use. 

"In  obeying  and  construing  these  rules,  due  regard  shall 
be  had  to  all  dangers  of  navigation  and  collision,  and  to 
any  special  circumstances  which  may  render  a  departure 
from  the  above  rules  necessary  in  order  to  avoid  immediate 
dangers." 


Article  6. 


A.  and  B.  are  hidden  from  each  other  by  the  high  land ; 
Eule  V  directs  that  in  this  situation  either  vessel  having 
arrived  within  half  a  mile  of  the  turn  shall  blow  1  long 
blast  wnich  shall  be  answered  by  a  similar  blast  by  any  ap- 
proaching vessel  within  hearing.  Suppose  A.  has  arrived 
within  the  half  mi?e  limit,  he  blows  1  long  blast  which  B. 
answers  with  a  similar  blast ;  then  the  passing  signals  are 
given  by  either  and  answered.  In  deciding  which  passing 
signal  to  give,  the  tide  conditions  and  nature  of  the  channel 
are  taken  into  consideration.  This  is  the  only  situation  in 
which  the  law  authorizes  the  use  of  the  passing  signals  when 
the  vessels  are  not  in  sight  of  each  other. 


(65) 


This  rule  and  signal  apply  to  the  case  in  which  a  steamer 
may  be  leaving  her  dock  and  other  vessels  may  be  approach- 
ing from  any  direction,  but  when  she  is  clear  of  her  berth 
and  fully  in  sight,  the  steering  and  sailing  rules  apply. 

Channel  Line. 


B 


A.  blows  1  long  whistle  in  leaving  the  dock ;  when  fully 
in  sight  of  B.  and  C.  and  clear  of  her  berth,  or  about  at  the 
X,  then  the  sailing  rules  apply,  and  the  proper  signals  are 
exchanged  according  to  the  direction  A.  intends  to  take. 

A.  ought  not  to  leave  until  channel  is  clear,  but  if  she  does, 

B.  and  C.  should  stop  until  A.  's  direction  is  determined. 


Article  7. 


Fog  Situations. 


North 


Close   hauled 
port  tack. 


Wind  S.  E. 


Dense  fog ;  so  of  course  we  assume  that  A.  cannot  see  B. ; 
but  A.  suddenly  hears  2  blasts  of  a  fog  horn  right  ahead; 

(66) 


he  knows  first  that  a  sailing  vessel  is  ahead  of  him,  distance 
off  unknown ;  he  knows  second  that  she  is  on  the  port  tack 
and  may  be  heading  anywhere  from  close  hauled  to  a  point 
where  the  wind  is  abeam,  for  with  the  wind  abaft  the  beam, 
he  would  blow  3  blasts.  Reasoning  that  a  yacht  close  hauled 
might  head  up  to  within  four  points  of  the  wind,  while  a 
square  rigger  would  need  six,  he  establishes  at  once  the  first 
point  on  which  she  may  be  heading  as  S.  or  four  points  from 
S.  E.  Then  counting  eight  points  from  S.  E.,  he  fixes  S.  W.  as 
the  other  possibility;  because  heading  S.  W.  the  wind,  if 
S.  E.,  would  be  abeam  which  establishes  the  limits  of  heading 
while  blowing  a  2  blast  signal,  viz.  between  S.  and  S.  W. 
Having  arrived  at  this  conclusion  almost  the  instant  he  hears 
the  two  blasts,  for  this  whole  process  of  reasoning  is  gone 
through  with  instinctively  and  instantaneously,  A.  ports  a 
point  or  two  until  safely  passed. 


Article  8. 


North 


Close  hauled  on 
Starboard  tack. 


Wind  S.  E. 


In  this  situation  B.  blows  1  blast  and  passing  through 
the  same  reasoning  as  before,  A.  finds  that  she  may  be  close 
hauled  on  starboard  tack,  perhaps  heading  up  as  high  as 
East;  or  that  she  may  have  the  wind  abeam  in  which  case 
she  would  be  steering  N.  E. ;  therefore  she  may  be  between 
E.  and  N.  E.  so  A.  starboards  a  point  or  two,  or  until  he 
brings  the  sound  of  the  horn  well  on  his  starboard  bow. 

(67) 


Article  9. 


North 


Running   with   a 
quartering  breeze. 
Wind  S.  E. 


This  is  a  more  doubtful  position  than  the  others,  for 
while  the  headings  in  Articles  7  and  8  can  be  determined 
within  four  points,  this  one  can  be  anywhere  in  sixteen  points. 
B.  blows  3  blasts  but  A.  at  first  is  in  doubt  and  stops  until 
by  subsequent  signals  he  can  determine  nearly  the  heading. 
The  reasoning  is  like  this:  At  N.  E.  ^  N.,  B.  would  begin 
blowing  3  blasts  and  should  continue  that  same  signal  on 
any  heading  between  there  and  S.  W.  a/4  W. ;  so  if  B.  is 
heading  at  any  sharp  angle  with  A.  's  course,  A.  will  soon 
detect  it,  for  the  succeeding  blasts  of  B.'s  horn  will  sound 
more  and  more  on  the  bow ;  but  if  the  sound  seems  to  remain 
about  ahead,  A.  will  figure  that  B.'s  course  is  nearly  on  a 
line  with  his  own  and  will  start  ahead  again,  either  star- 
boarding or  porting  a  little  as  he  thinks  best ;  keeping  a 
sharp  lookout  and  listening  for  the  echo  of  his  whistle  on 
B.'s  sails.  Always  proceed  with  caution  in  this  situation 
until  sure  of  B.'s  course.  Sometimes  it  is  a  little  help  on  the 
coast  to  judge  of  the  probable  course  of  B.  by  the  coast  line; 
if  there  are  no  harbors  in  the  vicinity,  or  special  turning- 
points,  it  is  fair  to  assume  that  B.  is  following  a  course  some- 
what in  line  with  A,  but  this  cannot  be  an  infallible  rule. 


(68) 


Article  10. 


North 


Running  with  wind 
on  port  quarter. 


Wind  N.  E. 

Here  is  the  worst  fix  A.  can  get  into  with  a  sailing  vessel, 
especially  if  there  is  any  wind.  B.  is  heading  towards  A., 
only  A.  can't  determine  that  heading  within  sixteen  points: 
it  may  be  anywhere  from  N.  W.  %  W.  to  S.  E.  ^4  S.  and  he 
may  not  have  time  to  take  the  bearing  of  B.  's  horn,  perhaps 
before  a  second  signal  is  blown  they  may  be  together.  Now 
what  had  A.  better  do?  If  he  starboards  his  helm,  it  will 
prove  all  right  if  B.  happens  to  be  heading  between  S.  and 
S.  E. ;  but  suppose  he  isn't  ?  Suppose  he  is  heading  S.  S.  W.  ? 
A.  has  then  made  a  fatal  mistake,  for  he  is  hauling  across 
B.'s  bow,  and  it  may  prove  the  same  if  A.  ports  his  helm. 
And  so  he  cannot  for  a  moment  think  to  either  starboard  or 
port  two  or  three  points  and  then  steady,  but  he  should  at 
once  throw  his  helm  hard  over,  one  way  or  the  other,  he 
can't  tell  which  will  be  the  best  unless  his  boat  swings  a 
little  quicker  on  one  helm  than  the  other,  and  keep  it  there 
till  he  brings  the  next  blast  so  far  'abaft  his  beam  that  the 
danger  is  over,  when  he  gradually  hauls  back  to  his  course. 
In  a  situation  of  this  kind,  don't  hesitate  an  instant,  but 
get  the  wheel  over.  Of  course  in  a  channel  such  a  course 
need  not  be  followed  for  the  probable  heading  of  B.  could 
be  established  with  a  fair  degree  of  accuracy,  but  out  on 
the  coast  or  ocean  it  is  a  very  different  affair.  It  is  essential 
that  the  terms  starboard  and  port  tack  are  understood  or 
the  signals  may  be  given  wrong,  or  misinterpreted.  The  tack 
a  vessel  is  on  is  named  according  to  the  side  the  wind  is  com- 
ing from,  viz. :  Starboard  tack  means  that  she  has  the  wind 
on  her  starboard  side.  Many  believe  just  the  opposite,  that 
it  is  named  according  to  the  side  the  booms  are  on;  but 
this  is  an  error  and  spells  disaster  if  followed. 

(69) 


Article  11. 


North  Red  Light  £   ^-<^~T: — •> 


A.  suddenly  makes  a  red  light  about  ahead  and  knows 
at  once  that  he  must  port  a  little  until  he  brings  it  out  clear 
on  his  own  port  bow. 

In  the  head  and  head  situation  A.  would  see  both  side 
lights,  therefore  he  establishes  S.  (a  little  Westerly)  as  the 
first  point  of  B.  's  possible  heading ;  and  as  a  side  light  shows 
two  points  abaft  a  vessel's  beam,  it  is  at  once  evident  that 
W.  N.  W.  would  be  the  last  possible  point  that  B.  could  be 
on,  or  count  10  points  to  the  right  of  S.  Therefore  A.  knows 
at  once  that  B.  must  be  heading  between  S.  (a  little  Westerly) 
and  W.  N.  W.  and  cannot  be  crossing  his  course ;  but  as  the 
angle  between  them  may  be  very  small,  A.  ports  as  described 
above  in  order  not  to  crowd  B. 


Article  12. 


In  this  situation  it  is  the  green  light  that  A.  makes 
ahead,  so  of  course  he  starboards  a  little  until  it  is  out  clear 
on  his  own  starboard  bow.  The  line  of  reasoning  to  be  fol- 
lowed is  the  same  as  in  Art.  11,  whereby  the  two  possible 
limits  of  heading  of  B.  are  established  as  S.  (a  little  Easterly) 
and  E.  N.  E.  when  his  light  would  shut  in  altogether ;  or 
count  ten  points  to  the  left  of  S. 

(70) 


Article  13. 


North  ffF    Dark  shadow, 

all  that  A  sees. 


Here  A.  sees  the  shadow  of  B.'s  hull  or  sails  without 
being  able  to  at  once  determine  his  heading. 

As  at  W.  N.  W.  the  red  light  became  invisible,  Art.  11, 
and  at  E.  N.  E.  the  green  light  disappeared,  Art.  12,  it  is 
obvious  that  the  dark  angle  is  from  W.  N.  W.  through  N. 
to  E.  N.  E.,  or  sixteen  points.  Quite  a  long  range  of  possible 
headings  and  unless  the  actual  one,  or  near  it,  is  immediately 
determined,  A.  should  throw  his  helm  hard  over,  one  way  or 
the  other,  to  be  determined  by  which  side  there  is  the  most 
room  and  by  which  helm  his  boat  handles  the  more  quickly 
on,  and  keep  it  there  till  B.  is  far  enough  on  his  bow  as  to 
render  a  collision  impossible;  then  steady  and  haul  back 
gradually  to  his  course.  If  there  isn't  room  to  do  this,  stop 
and  back  at  once  until  B.'s  heading  can  be  more  accurately 
determined. 

In  either  Art.  11,  12  or  13,  if  the  light  or  shadow  is  made 
out  on  either  bow,  hastily  determine  the  bearing  and  reverse 
it  for  one  of  the  limits  of  heading  and  count  the  ten  or  sixteen 
points  as  the  case  may  be  to  determine  the  other  limit.  For 
example,  suppose  in  Art.  11,  B.  bore  three  points  on  A.'s 
starboard  bow  or  N.  E.  x  N.,  the  opposite  point  is  S.  W.  x  S. 
when  both  side  lights  would  appear,  therefore  S.  W.  x  S.  (a 
little  Westerly)  is  one  limit  and  ten  points  to  the  right  or 
N.  W.  x  N.  is  the  other  limit. 

In  that  case,  A.  would  have  to  act  quickly  and  throw  his 
helm  hard  a  port  to  bring  B.  on  his  port  bow. 


(71) 


CHAPTER  EIGHT. 


A    Little    Old    Junk. 


To  Mark  a  Lead  Line. 

2  fathoms,  2  strips  of  leather 

3  «         3 

5  white  rag 

7  red  rag 

10  leather  with  one  hole 

12  same  as  2 

13  blue  rag,  or  same  as  3 
15  same  as  5 

17  it  it  (  (.      rj 

20  leather  with  2  holes 

25  1  knot 

30  3  knots 

35  1  knot 

40  4  knots 

45  1  knot 

50         "         5  knots 

Always  mark  the  line  wet  and  attach  the  lead  to  be  used. 

Arming  —  This  is  soap  filled  into  a  hole  in  bottom  of  lead 
to  bring  up  a  sample  of  the  bottom. 

To  open  a  coil  of  new  rope,  laid  and  coiled  right  handed. 
Use  the  inside  end  and  coil  left  handed  in  a  large  coil, 
leaving  the  bottom  end  in  the  center,  when  coiled  once 
bring  the  bottom  end  up  through  the  center  and  again 
coil  left  handed;  bring  the  end  up  once  more  and  coil 
right  handed. 

(72) 


How  to  Construct  a  Drag  —  If  for  small  boats  or  launches, 
lash  together  the  oars,  weight  them,  with  the  anchor, 
make  fast  your  anchor  rope  and  pay  out,  keeping  the 
inboard  end  fast  forward,  the  purpose  being  to  keep  her 
head  to  the  sea  if  it  is  too  heavy  to  run.  If  there  are 
no  oars,  use  anything  at  hand,  such  as  gratings,  deck 
chairs  or  settees. 

Collision  mat  —  This  may  be  any  piece  of  canvas  drawn 
down  over  a  hole  below  the  water  line.  Make  a  rope 
fast  to  each  corner  of  a  square  of  canvas  and  haul  it 
over  the  hole  which  may  some  times  have  a  pillow, 
blanket  or  mattress  stuffed  into  it  first.  Your  boat  may 
be  saved  from  sinking  by  using  a  little  ingenuity. 

Use  of  Oil  in  Rough  Water  —  If  the  sea  is  so  rough  as  to 
be  dangerous  in  running,  take  a  potato  sack,  a  canvas 
bag  with  holes  punched  in  the  bottom  is  better,  put  in 
a  good  sized  wad  of  oakum  or  waste  and  saturate  it 
with  oil.  Hang  this  over  the  side  and  the  constant  drip- 
ping of  oil  will  form  a  slick  near  the  boat  so  she  can 
run  with  perfect  safety.  If  hove  to  and  shipping  water 
it  is  just  as  valuable. 


(73) 


Points  of  the  Compass  —  They  are  32  in  number,  sub-divided 

into  %  and  1/4  points. 


N.  i/4  E. 

N.  N.  E.  14  E. 

N.  E.  14  E. 

E.  N.  E.  14  E. 

N.  1/2  E. 

N.  N.  E.  i/2  E. 

N.  E.  i/2  E. 

E.  N.  E.  !/2  E. 

N.  3/4  E. 

N.  N.  E.  3/4  E. 

N.  E.  3/4  E. 

E.  N.  E.  3/4  E. 

N.xE. 

N.  E.  x  N. 

N.E.xE. 

E.xN. 

N.  x  E.  1/4  E. 

N.  E.  3/4  N. 

N.  E.  x  E.  %  E. 

E.  3/4  N. 

N.  x  E.  1/2  E. 

N.  E.  i/2  N. 

N.  E.  x  E.  1/2  E. 

E.  1/2  N. 

N.  x  E.  %  E. 

N.  E,  %  N. 

N.  E.  x  E.  3/4  E. 

E.  %  N. 

N.  N.  E. 

N.E. 

E.  N.  E. 

E. 

E.  %  S. 

S.  E.  xE.  3/4  E. 

S.  E.  %  S. 

S.xE.  3/4  E. 

E.  i/2  S. 

S.  E.  x  E.  1/2  E. 

S.  E.  1/2  S. 

S.  x  E.  1/2  E. 

E.  3/4  S. 

S.  E.  x  E.  %  E. 

S.  E.  3/4  S. 

S.xE.  %  E. 

E.xS. 

S.E.xE. 

S.  E.  x  S. 

S.xE. 

E.  S.E.  3/4  E. 

S.  E.  3/4  E. 

S.  S.  E.  3/4  E. 

S.  3/4  E. 

E.  S.  E.  -72  E. 

S.  E.  1/2  E. 

S.  S.  E.  1/2  E. 

S.  1/2  E. 

E.  S.  E.  %  E. 

S.  E.  i/4  E. 

S.  S.  E.  i/4  E. 

S.  1/4  E. 

E.  S.E. 

S.E. 

S.  S.  E. 

S. 

S.  1/4  W. 

S.  S.  W.  i/4  W. 

s.  w.  1/4  w. 

w,  s.  w.  1/4  w. 

S.  1/2  W. 

S.  S.  W.  i/2  W. 

S.  W.  1/2  W. 

W.  S.  W.  1/2  W. 

S.  3/4  w. 

s.  s.  w,  3/4  w. 

s.  w.  3/4  w. 

w.  s.  w.  3/4  w. 

S.xW. 

S.  W.  x  S. 

S.  W.  x  W. 

W.xS. 

S.  x  W.  14  W. 

S.  w.  3/4  s. 

S.  W.xW.  i/4  W. 

w.  34  s. 

S.  x  W.  i/2  W. 

S.  W.  1/2  S. 

S.W.  x  W.i/2  W. 

W.  1/2  S. 

S.  x  W.  3/4  W. 

s.  w.  14  s. 

S.W.  x  W.3/4  W. 

w.  14  s. 

S.  S.  W. 

s.w. 

w.  s.  w. 

w. 

W.  14  N. 

N.W.  x  W.s/i  W. 

N.  W.  %  N. 

N.  x  W.  3/4  W. 

W.  1/2  N. 

N.WxW.i/2;W. 

N.  W.  1/2  N. 

N.  x  W.  1/2  W. 

W.  %  N. 

N.W.X  W.i/4  W. 

N.  W.  3/4  N. 

N.  x  W.  %  W. 

W.  x  N. 

N.  W.  x  W. 

N.  W.  x  N. 

N.xW. 

W.N.W.3/4  W. 

N.  w.  3/4  w. 

N.  N.  W.  3/4  W. 

N.  3/4  w. 

W.N.W.i/2  W. 

N.  W.  1/2  W. 

N.  N.  W.  1/2  W. 

N.  1/2  W. 

W.N.W.i/4  W. 

N.W.  14  W. 

N.  N.  W.  %  W. 

N.  14  W. 

W.  N.  W. 

N.W. 

N.  N.  W. 

N. 

To  box  the  compass  is  to  learn  the  32  whole  points  be 
ginning  N.  x  E.,  and  then  to  say  them  backwards. 

(74) 


Placing  the  Compass  —  If  there  is  no  standing  binnacle,  have 
cleats  fastened  to  the  deck  in  the  handiest  place  for  the 
one  steering,  so  that  the  compass  is  always  in  line  with 
the  keel,  although  it  need  not  necessarily  be  amidships. 
Also  select  a  place  as  far  as  possible  from  any  magnetic 
metal  especially  if  it  is  movable.  If  any  fog  running 
is  to  be  done,  this  is  most  important. 

To  Anchor  —  Pick  out  your  spot  and  bring  her  head  to  it; 
notice  how  the  other  boats  are  tailing.  Stop  early  and 
let  her  way  take  her  up,  then  if  the  tide  doesn't  suf- 
ficiently check  her,  give  her  a  kick  back  and  when  she 
gathers  stern  board  let  go,  and  stop  her.  In  letting  go 
under  head  way,  she  will  run  up  over  the  anchor  and 
when  she  straightens  back,  the  cable  may  come  foul 
perhaps  tripping  the  anchor;  therefore  this  should  be 
avoided  as  much  as  possible. 

To  Run  Cut  a  Kedge  Anchor  —  Haul  your  boat  up  to  where 
the  anchor  is  being  lowered  and  see  that  it  has  a  long 
lashing  in  the  ring,  long  enough  to  more  than  reach 
round  your  boat ;  and  if  you  wish  to  trice  it  up  for 
shoal  water,  have  another  on  the  crown;  lower  the 
anchor  into  the  water  and  pass  one  part  of  the  lashing 
under  the  boat;  bring  the  two  parts  together  and  tie 
them,  allowing  the  anchor  to  hang  down  amidships. 
Coil  as  much  of  the  hawser  into  your  boat  as  you  can 
conveniently  and  run  out  in  the  desired  direction,  pull- 
ing the  hawser  first  off  the  ship  ?s  deck ;  when  that  is 
all  out,  pay  overboard  from  your  coil  until  the  end  when 
the  anchor  lashing  is  cut.  If  you  have  a  boat  under 
oars,  instead  of  a  motor,  make  the  ring  lashing  fast  to 
the  stern.  If  the  water  is  shoal,  haul  up  on  the  crown 
lashing,  making  it  fast  around  the  boat  and  up  over  the 
gunwales,  which  will  carry  the  anchor  more  in  line  with 
the  keel  instead  of  perpendicular  to  it,  and  also  dis- 
tributes the  weight. 

Bell  Signals  to  the  Engine  Room  —  From  a  stop,  1  bell,  slow 
ahead.  Jingle,  full  speed.  1  bell  to  slow  down,  1  more 
to  stop.  2  bells  to  back,  jingle,  full  speed  astern ;  then  1 

(75) 


bell  stops.    From  full  speed  ahead  to  full  speed  astern, 
4  bells  and  a  jingle. 

Study  a  Coast  —  If  entering  a  strange  harbor  or  coming  on 
to  a  piece  of  coast  that  is  new  to  you,  make  a  study  of 
it  beforehand,  don't  wait  till  you  get  there.  Get  a  gen- 
eral idea  of  the  outline  of  the  land,  whether  high  or  low, 
look  up  the  soundings  giving  special  attention  to  any 
dangerous  shoals  or  reefs,  find  in  the  lighthouse  book 
the  description  of  any  lighthouses  or  lights  with  their 
fog  signals,  and  keep  the  book  at  hand  to  refresh  your 
memory  when  needed.  If  you  have  a  * '  Coast  Pilot, ' '  look 
up  what  is  said  about  this  particular  place,  with  special 
reference  to  the  tides,  strength  of  current,  etc.  Have 
your  chart  and  lead  at  hand  and  keep  a  good  lookout. 

Buoys  —  The  general  rule  is  in  entering  a  harbor,  red  to 
starboard  and  black  to  port ;  black  and  red  horizontal 
stripes  mark  an  obstruction  in  a  channel,  go  either  side 
and  give  it  a  good  berth.  Black  and  white  perpendicular 
stripes  are  on  channel  buoys,  meaning  mid  channel, — 
pass  close  to  them ;  anchor  buoys  are  white  and  are 
generally  placed  according  to  local  conditions,  giving 
vessels  a  chance  to  anchor  back  of  them,  leaving  the 
channel  free.  This  description  of  the  painting  applies 
to  any  type  of  buoy,  the  spar,  a  long  straight  stick ;  nun, 
a  cone ;  can,  a  cylinder ;  whistling,  tall  type  nun  sur- 
mounted by  a  whistle ;  bell,  generally  a  cage  with  a 
bell  at  top ;  gas,  similar  to  the  whistling,  only  instead 
of  the  whistle  at  the  top  has  a  lantern.  Where  nun  and 
can  buoys  are  used,  the  nuns  are  usually  red  and  the 
cans  black.  Passing  through  a  sound  or  roadstead  from 
the  E.  toward  the  W.,  the  buoys  will  be  found  as  in 
entering  a  harbor.  Red  buoys  all  have  even  numbers, 
black  buoys,  odd  numbers. 


(76) 


To  Mark  a  Chip  Logline  —  This  was  the  method  in  use  for- 
merly to  ascertain  the  speed  of  the  ship  and  the  line  was 
marked  by  this  example  in  proportion : 

3600s  :  6086  ft.   :  :  28  :  47.33  ft. 

Therefore  with  a  line  marked  for  a  23  second  glass, 
a  knot  is  47  feet,  4  inches  long.  An  amount  of  stray 
line  was  left  next  the  chip  which  was  weighted  on  one 
edge  to  stand  upright  in  the  water,  marked  by  a  piece 
of  red  bunting,  and  each  length  of  47  feet,  4  inches  after 
that  by  a  piece  of  fish  line  with  one,  two  or  three,  etc., 
knots  in  it,  according  to  its  number  from  the  "stray 
line."  Each  knot  was  subdivided  into  five  equal  parts 
and  a  small  piece  of  white  bunting  turned  into  the  line 
at  every  two-tenths  division  thus  formed.  The  chip  is 
thrown  over  and  when  the  "Stray"  goes  over  the  rail, 
the  officer  cries  "Turn"  and  whoever  holds  the  glass 
turns  it,  allowing  the  sand  to  begin  running;  when  it 
has  all  run  through  he  cries  "Stop"  and  the  officer  snubs 
the  line  at  once,  counting  up  the  knots  and  tenths.  If 
the  vessel's  speed  was  greater  than  4  knots,  the  fourteen 
second  glass  was  used  instead  of  the  28,  and  the  number 
of  knots  run  out  was  doubled.  The  28  and  14  second 
glasses  were  called  respectively  the  long  and  short  glass- 
es. This  practice  of  measuring  a  ship's  rate  of  sailing 
is  founded  upon  the  principle  that  the  length  of  each 
knot  is  the  same  part  of  a  sea  mile  as  twenty-eight  sec- 
onds is  of  an  hour;  it  was  much  in  vogue  a  few  years 
ago  but  with  the  advent  of  fast  steamships  and  the 
patent  log  it  is  practically  extinct. 

Strength  of  Rope  —  The  strength  of  a  rope  yarn  of  medium 
size  is  100  Ibs.,  but  the  twist  given  it  in  laying  up  di- 
minishes its  strength  after  certain  limits  so  that  it  varies 
from  76  Ibs.,  in  a  12  in.  rope  to  104  Ibs.,  in  %  inch  rope. 

A  Practical  Rule  for  Ascertaining  the  strength  of  rope.  The 
square  of  half  the  circumference  gives  the  breaking 
strain  of  the  weakest  plain  laid  rope  in  tons,  and  is 
therefore  a  safe  rule. 


To  Ascertain  the  Weight  of  Rope  — Three  strand,  plain  laid, 
25  thread  yarn,  tarred ;  multiply  the  square  of  the  cir- 
cumference by  the  length  in  fathoms,  and  divide  by  4.24 
for  the  weight  in  pounds. 

A  practical  rule  for  determining  the  relative  strength  of 
chain  and  rope.  Using  the  diameter  of  the  chain  and  the 
circumference  of  the  rope,  consider  the  proportionate 
strength  of  chain  and  rope  to  be  10  to  1.  Half  inch 
chain  may  therefore  replace  5  inch  rope.  The  breaking 
strain  of  chain  may  be  found  by  dividing  the  square  of 
the  diameter  in  eighths,  by  2.4  for  round  link  chain,  and 
by  2.7  for  chain  cable. 

To  find  the  weight  a  rope  will  lift  when  rove  as  a  tackle. 
Multiply  the  weight  the  rope  will  sustain  by  the  number 
of  parts  at  the  movable  block,  and  subtract  y±  of  product 
for  resistance. 

To  find  the  size  of  rope  when  rove  as  a  tackle  to  lift  a  given 
weight.  Divide  the  weight  to  be  raised  by  the  number  of 
parts  at  the  movable  block  to  get  the  strain  on  a  single 
part;  add  %  of  this  for  the  increased  strain  due  to 
friction,  and  reeve  the  rope  of  the  corresponding 
strength. 

To  find  what  number  of  parts  of  a  small  rope  are  equal  to 
a  large  rope.  Divide  the  square  of  the  circumference 
of  the  larger  rope  by  the  square  of  the  circumference  of 
the  smaller,  and  the  result  will  be  the  number  of  parts 
of  the  smaller  equal  to  one  part  of  the  larger. 

Strength  of  Cotton  Canvas  —  Cotton  canvas  is  22  inches 
wide  and  contains  80  running  yards  to  the  bolt.  In  No.  's 
1,  2  and  3,  the  blue  thread  must  be  1%  inches  from  the 
selvage ;  in  No.  's  4,  5  and  6,  l1/^  inches ;  in  No.  's  7  and 
8,  1  inch ;  in  No.  's  9  and  10,  %  of  an  inch.  In  testing, 
three  strips  crosswise  and  three  strips  lengthwise  are 
cut;  the  strips  to  be  each  1  inch  wide  and  22  inches 


(78) 


long  except  in  No.'s  8,  9  and  10,  which  iv'iil  be  cut  1% 
inches  wide  and  22  inches  long. 

Number  of  Pounds  Weight  Pound  Weight  Borne  by  Strips 

Canvas.  Per  Bolt.  Crosswise.  Lengthwise 

1  90  280  250 

2  85  260  230 

3  80  240  210 

4  75  230  200 

5  70  220  190 

6  65  210  180 

7  60  200  170 

8  55  220  190 

9  50  210  180' 
10  45  200  170 

Helm  —  The  term  Starboard  and  Port  refer  to  the  helm,  or 
tiller  and  not  the  wheel.  With  the  wheel  ropes  rove 
straight  and  tiller  forward  of  the  rudder,  throwing  the 
wheel  to  port  pulls  the  tiller  to  starboard  and  the  boat's 
head  goes  to  port ;  therefore  starboarding  the  helm  in 
that  case  means  putting  the  wheel  to  port  and  vessel's 
head  to  port.  Now  suppose  the  wheel  ropes  are  rove 
crossed,  to  pull  the  tiller  to  starboard,  the  wheel  must 
be  rolled  to  starboard  and  the  boat's  head  goes  to  port 
as  before.  Hence  the  order  to  Starboard  means  that  the 
boat's  head  shall  be  directed  to  port;  and  the  order  to 
Port  that  she  shall  be  directed  to  starboard.  In  taking 
charge  of  a  strange  vessel,  one  of  the  first  things  to  de- 
termine is  the  effect  on  the  vessel's  bow  of  turning  the 
wheel  in  eiher  direction.  All  outside  ships  have  their 
wheel  ropes  rove  straight  so  that  the  order  to  Starboard 
means  throw  the  wheel  to  port;  the  vessel's  head  goes 
same  as  the  wheel.  In  many  inland  boats  the  practice 
is  just  the  reverse. 

The  statements   relative   to   rope,  chain,  etc.,  taken   from  "Luce's 
Seamanship." 

(79) 


A  FEW  DON'TS. 


Don't  depend  too  much  on  what  someone  else  does;  he  maj 
be  wrong. 

Don't  play  the  road  hog. 

Don't  cross  the  other  fellow's  bow  just  to  show  off;  your 
motor  might  stick  and  a  collision  result. 

Don't  place  your  compass  near  any  magnetic  metal. 

Don 't  blow  about  never  having  had  an  accident ;  it  is  liable 
to  be  a  boomerang. 

Don't  fail  to  answer  signals. 
Don't  use  cross  signals. 

Don 't  be  ashamed  to  use  caution ;    slow  or  stop  in  time. 
Don't  run  full  speed  in  a  fog. 

Don't  present  your  broadside  if  you  see  a  collision  is  in- 
evitable ;  in  the  time  you  have,  swing  towards  him  and 
you  are  not  as  liable  to  be  sunk ;  this  is  in  case  there  is 
no  chance  to  wiggle  round  him. 

Don't  be  dead  sure  to  the  point  of  recklessness;  the  safe 
navigator  believes  it  possible  to  make  a  mistake. 

Don't  forget  to  take  your  running  lights  with  you,  even 
though  you  intend  to  return  before  sunset ;  your  plans 
may  get  a  kink  in  them. 


(80) 


"" 


AN  INITIAL  PINE  OP  25  CENTS 


YB  04380 


359891 


***&'*. 


UNIVERSITY  JOF  CALIFORNIA ttBRARY'  * 


